Any chance it can be fixed. the back of seat does lock in horizontal position or do I need a new seat

by slamming the seat back when the clip was down , you may have bent the clip
it may require pliers or lever to lift the clip back up into position

BCM has nothing to do with this function , MMM - memory mirror module !
Memory Mirror System Operation
The MMM is capable of storing mirror position for 2 different drivers. Mirror position is determined by both horizontal and vertical position sensors in each of the power mirrors. The MMM supplies a reference voltage and a low reference to these sensors and determines mirror position through the horizontal and vertical position signal circuits.
The MMM receives power through the battery supply voltage circuit and the MIR/LOCK fuse and a constant ground source. Any time that battery voltage is disconnected and then connected from the MMM, the MMM will enter the mirror relearn mode. The mirror relearn mode can also be commanded using a scan tool. Refer to Memory Mirror Module Learn for further information.The memory switch receives power through the battery supply voltage circuit and the MIR/LOCK fuse. The MMM upon receipt of a memory switch signal input, a class 2 message from the SIC or a class 2 message from the PCM indicating that the transmission is in park, will then supply battery voltage and ground to the appropriate power mirror motors through the mirror motor control circuits to move the mirrors to the predetermined positions.

DTC B1586, B1596, B1616, or B1626
The mirror horizontal and vertical position sensors are potentiometers. The Memory Mirror Module (MMM) provides these sensors with a 5 volt reference circuit and a low reference circuit. The MMM monitors the horizontal and vertical position sensor signal circuits which change values based on mirror position. These voltage values are used to determine mirror position and can be set into memory. When the MMM receives a memory recall request, the MMM will control the power mirror to the memory position based on the horizontal and vertical position sensor signal values.

Install a scan tool.
Turn ON the ignition, with the engine OFF.
With the scan tool, observe the mirror horizontal and vertical position parameters in the Memory Mirror Module (MMM) data list.
Operate both the left and right mirrors through the full range of movements.
Does the scan tool indicate that the left and right mirror horizontal and vertical position parameters are within the specified range?

Memory Seat System Components
The memory seat system consists of the following components:
• Power seat switch assembly
• Memory recall switch assembly
• Horizontal adjuster motor
• Front vertical adjuster motor
• Rear vertical adjuster motor
• Recline adjuster motor
• Memory seat module
• Memory mirror module
• SEAT 25A circuit breaker
• MIR/LOCK 3A fuse

Your best bet , take it to a qualified repair shop !

Check the spring which puts tension on the lever to hold it in the lock position this may have dislodged itself or be broken or possibly bent.

You don't mention what year your Yukon is ? This could very well be a control Module problem .
I'll post how the power memory seat's work or are suppose to work !

Memory Seats Description and Operation

Battery voltage is supplied to the memory seat module through a 25 A circuit breaker. The memory seat module supplies the seat adjuster switch assembly with a battery positive reference voltage. While the seat adjuster switches are in an inactive state the switch contacts are closed to the adjuster switch common circuit. When a seat adjuster switch is pressed to an active state the switch contact is closed to the reference voltage circuit. Battery voltage on a switch signal circuit indicates to the memory seat module the switch status is active. Each seat adjuster motor is controlled by the memory seat module through 2 motor control circuits. While the seat adjuster motors are in an inactive state the motor control circuits are closed to ground circuit contacts within the memory seat module. The memory seat module operates the seat adjuster motors by switching one of a motors control circuits to battery voltage. The seat adjuster motors are bidirectional and the direction of adjuster motor rotation is determined by which of the adjuster motor control circuits is switched to battery voltage while the other remains grounded.


Memory Set/Recall Operation
The seat adjuster motors are equipped with internal position sensors. The adjuster motor position sensors are monitored by the memory seat module and are used to determine the seat position when storing or recalling memory settings. The driver seat adjuster motors use potentiometer type position sensors. The position sensors are supplied with a 5 V reference and ground circuits from the memory seat module. The position sensor signal circuits return to an analog input within the memory seat module. During adjuster motor operation the position sensor provides a voltage change proportional to the change in revolution of the adjuster motor shaft. The memory seat module monitors the voltage from the position sensor signal circuits to determine the adjuster motor positions when storing or recalling memory seat position settings.
The memory recall switch assembly on the driver door provides inputs to the driver door lock/window switch. Battery voltage is supplied to the memory recall switch assembly from the driver door lock/window switch. When a RCL 1, RCL 2, or EXIT switch is pressed, the switch contacts close the appropriate switch signal circuit to the battery voltage supply circuit within the memory recall switch assembly. When the driver door lock/window switch receives active switch signals from the memory recall switch assembly, the appropriate commands are sent to the memory seat module using the GMLAN Serial Data circuit. The Body Control Module software version determines the personalization features available.
Memory seat recall operation is allowed only with the transmission selector lever in the PARK position while the ignition is on. The transmission selector lever position data is provided to the memory seat module by a message through the GMLAN Serial Data circuit.

There are somethings listed you are not familiar with , like GMLAN Serial Data circuit ,maybe Body Control Module software etc... GMLAN is a communincation network that the computers on the vehicle uses to share information , transmit commons etc... you can google it to read about it .

There are DTC'S - diagnostic trouble codes that can set in the module in control . Do you know what DTC'S are .

DTC Descriptors
DTC B1825 01: Driver Seat Recline Position Sensor Circuit Short to Battery
DTC B1825 06: Driver Seat Recline Position Sensor Circuit Short to Ground or Open
DTC B1825 5A: Driver Seat Recline Position Sensor Circuit Plausibility Failure
DTC B1850 01: Driver Seat Lumbar Horizontal Position Sensor Circuit Short to Battery
DTC B1850 06: Driver Seat Lumbar Horizontal Position Sensor Circuit Short to Ground or Open
DTC B1850 5A: Driver Seat Lumbar Horizontal Position Sensor Circuit Plausibility Failure
DTC B1860 01: Driver Seat Lumbar Vertical Position Sensor Circuit Short to Battery
DTC B1860 06: Driver Seat Lumbar Vertical Position Sensor Circuit Short to Ground or Open
DTC B1860 5A: Driver Seat Lumbar Vertical Position Sensor Circuit Plausibility Failure
DTC B2355 01: Driver Seat Front Vertical Position Sensor Circuit Short to Battery
DTC B2355 06: Driver Seat Front Vertical Position Sensor Circuit Short to Ground or Open
DTC B2355 5A: Driver Seat Front Vertical Position Sensor Circuit Plausibility Failure
DTC B2365 01: Driver Seat Rear Vertical Position Sensor Circuit Short to Battery
DTC B2365 06: Driver Seat Rear Vertical Position Sensor Circuit Short to Ground or Open
DTC B2365 5A: Driver Seat Rear Vertical Position Sensor Circuit Plausibility Failure
DTC B2375 01: Driver Seat Assembly Horizontal Position Sensor Circuit Short to Battery
DTC B2375 06: Driver Seat Assembly Horizontal Position Sensor Circuit Short to Ground or Open
DTC B2375 5A: Driver Seat Assembly Horizontal Position Sensor Circuit Plausibility Failure

5) Memory Seat Module is under the front of the driver seat , you could look under an see if all the connectors are fully seated.

The best diagnostic step would be to hook up the factory scan tool an see what the computer is seeing as far as inputs from the switch an outputs it's sending . I wouldn't suggest you take the seat apart an try testing electrical inputs etc.... unless you very familiar with automotive electrical systems an circuits .

You can try to pull on the belt with the plastic trim piece removed the take a flat tipped screwdriver the release the arm or bar holding the belt in the lock position. Most of these have a spring on them. That spring can fall out. Or sometimes the bar or lock arm may be jammed and needs to be pried loose then lubricated to prevent this from repeating in the future.

i had this problem on my 96 chevy, basically theres a set of ratcheting gears that lock the seat in place in the various positions. sometimes over time or due to abuse one side or the other gets stripped out and the seat will no longer lock into place. i found a ripped up seat on Craigslist that was in a part out truck and bought it cheap then took both seats in the an upholstery shop, between the junked out seat (15 bucks) and the labor at the shop (50bucks) it cost me 65 bucks to fix, hope this helps

The manual lever to release the seat is supposed to have a spring on it to return the release lever to the lock position, if the lever does not spring back when you let go of the seat adjustment lever then you know there is a missing, dis-connected, or broken return spring.

If this is the case try putting the seat where you want it to be and make sure that the adjustment lever returns to the lock position, now check to see if the seat will lock in with the adjustment lever in the lock position.

If it does lock in repair or replace the return spring.

Make sure that the adjustment lever is attached to the locking linkage and it does move the locking mechanism.

If it still does not lock into place then there is something wrong with the seat locking mechanism, and some WD-40 sprayed onto the seat rails and track might release a stuck mechanism, and if everything seems to be working alright, and you can see that the locking mechanism in the seat rail is moving in and out of the lock position, then the locking tabs are most likely sheered off and you will need to replace the seat.

Also look under the drivers side seat and compare the lever position and the linkage connections with the passenger side seat, and make sure that it is all operating like the drivers side seat.

On W-Body vehicles, the front seats are secured to the floorpan by two front hook attachments and two rear bolts installed to nuts welded to the floorpan.
The manually operated two-way front adjusters provides only fore and aft movement of the seat. When the seat adjuster handle located on the front seat is pulled up, the seat adjusters unlock, permitting travel of the seat. When the seat is in the desired position and the seat adjuster handle is released, the seat locks in place.
A power operated six-way seat adjuster is available. The adjusters are activated by three 12 volt, reversible, permanent magnet motors with a built-in circuit breaker. The motors are energized by a switch bolted on the seat side panel.
The three motors drive the front seat and rear vertical actuators and a horizontal actuator. When the adjusters reach the limit of travel, torque is absorbed through the rubber mounted grommets located between the motor and the support. An overload relay is provided in the circuit and will open should excessive stall be applied.
The optional 60/40 split bench front seats have seat back head restraints on the driver's and passenger's seat back. The head restraints are designed so they cannot be removed from the seat back without first inserting a small rounded tool inside the head restraint support tube to release the locking tab. The 60/40 split bench seat is equipped with a reclining mechanism on both the driver's and passenger's side. The recliner lever is located on the outboard side of the spring cushion. When the lever is pulled upward, the spring loaded dual linear reclining unit located in the cushion frame is released, allowing the seat back to be pushed rearward or allowing the spring loaded reclining unit to bring the seat back forward.
Bucket seats are equipped with manual reclining mechanisms. An optional six-way power seat adjuster is available. Some bucket seats are equipped with inertia seat back locks. This system allows the seat back to fold forward without requiring the occupant to release a locking lever or access to the rear seat area. During a sudden stop or deceleration, or if the front of the vehicle is nose down, the inertia system of the seat back lock will engage, holding the seat back in its rest position. A release lever is provided to allow manual release of the seat back lock when the vehicle is in the nose down position. The release lever is located at the lower rear outboard corner of the seat back.
Some W-Body vehicles (notably Pontiac coupes) have passenger front seats equipped with an E-Z Entry device. This is actuated, in an unoccupied seat, by completely folding the seat back forward disengaging the adjuster, and sliding the front seat forward to gain access to the rear seat area. To return the seat to its normal position, return the seat back to its rest position, and slide the entire seat rearward, engaging the adjuster.
W-Body rear seats are available in several styles including a rear seat with an integral child restraint device.

would need car in front of me and my oil can in my hand to clean the mechanism of accumlated dirt around the springs and the whatever and a nice drop of real oil and not that fish oil od wd40

To fix that scenario, I have to get to the bolts anchoring the seat belt which can be found under the rear seat. Which a socket wrench, remove the bolt freeing the seatbelt to allow you room to release the lock to pull the belt out from the top of the back seat. You may now push the back seat into its upright position and then refasten the seatbelts with the bolt to it's former position under the back seat.

When I in later times need to lower the back seat, I will either loop the seatbelt around the head rest or tie two belts together allowing for slack in case the belt tightens again when trying to move the seat back to its original position.

.....Very frustrating!!!