2000 Chevrolet suburban rear heat & air

SOURCE: 1983 Chevrolet Suburban Heater fan not working

check relay and blower resistor...likely the relay is bad.

SOURCE: Rear a/c not blowing cold, front works fine.

you may not have enough refrigerant. a low charge can cause the rear in this dual system to not work for beans. charge with a can of uv and find the leak. fix the leak. evac the system and recharge. i think you take 4 lbs, but check the accumulator sticker. you may want to just change the accum at the same time.

SOURCE: 2007 Chevy Uplander Rear Overhead A/C Vents Won't Work

Have you checked the Aux switch near the bottom of the center control console.
There should be a knob with: Aux, Off, 1, 2, 3. This is the switch for the rear AC blower.
If the driver wants to control the rear AC, use the 1, 2, 3 settings.
If you put it on Aux, Than the rear AC is controlled by the passenger in the back seat using the extra controls located on the Overhead DVD player. (The front AC must be on the rear to work)

SOURCE: my Chevrolet suburban rear A/C is not working,

there is a line from under the hood freon manifold that runs under the vehicle to the rear evaporator and being under the vehicle it gets corroded and the freon escapes,you need to find the bad spot and go to an auto parts dealer and buy a "line-section" repair kit,then replace,then take it to a certified tech to evacuate the system and recharge it

SOURCE: 2005 Chevrolet Suburban Heater blow's

The most likely problem is, you have a trap door sticking in the duct system under the dash.
Unfortunately the only way to know for sure is to remove the panels between the bottom of the dash and the floor to visually inspect. If you have a dual zone/climate controll system, you have what's refered to as a split door system and those have been known to be problematic.
I hope this helps.