What cause the brakes to lockup

the brakes are fixed first.
a real brake shop finds the actual cause of that lockup. first !
it can be caused by many things or a very bad ABS modulator.
fix brakes first then ABS,
no abs in the the world can hide bad brakes, at tad weak yes.
cause (GENERIC)
ABS is telling you the brakes (actual ) are failing, and even you know that too. (locks up) if it locks up the sensor goes dead, ABS does not understand or like that ever, and says the sensor is dead but is al lie
kinda, no sensor is good ,just the pulsed of it are dead, and expected. for any lockup. like this.
so at the failing wheel the whole assembly is fully inspected for damage ,rust seizure or breakage.. and make sure ABS end is not causing the lockup.
even axle bearings.checked. LR axles.
forget ABS, fix brakes, test them first, fully and fully inpected.
and service brake failures here, all here LR checked

Brake light switch may be bad . Do the brake lights work ? Being stuck on may cause a no torque converter lockup situation and being not able to light up can cause non disengagement of the lockup solenoid .

When you say you've changed EVERYTHING, you mean brake pads, calipers, and rotors? Did you include the rubber brake hose to the caliper? Many people overlook this as a possible problem, yet it can cause lockups on occasion because the inner liner can collapse and act like a check valve.

dont drive this man killer, please.
the brake pedal is not comming all the way back or the brake rod
to rear of MC is not at spec clearance. this causes 4 wheel lockup
and this happened do to the rod there not allowing the mC piston
to unblock the relief ports.
see here, see them ports, open?, yours are not, and are a man killer.

http://static.howstuffworks.com/gif/master-brake3.jpg

If your brakes were "locking up" as you describe, it would be interesting to see. Brakes rarely self-apply. Lockup may occur after you apply the brakes as they may stick and won't release, but to have them just apply while driving is almost impossible. What you are describing sounds more to me like a massive vacuum leak. What this will do is reduce intake vacuum and steal all the power from the engine, and the brake pedal will go stiff as a result of the power brake booster losing its vacuum assist. You need to find the source of the vacuum leak and correct it.

It could be caused by a throttle body issue or an EGR valve problem, but it sounds more like your transmission torque converter clutch may be locking up. This can be cause several reasons. I'll list the most common. First check your transmission fluid. If its low it can cause the torque converter to lock up at low speeds. Next, if the transmission is a 545RFE the problem could be caused by the trans filter leaking at the seal. You will need to drop the trans pan and inspect the seal. There is a round filter and a flat one. The seal is up in the transmission where the flat filter plugs into the transmission. A new filter from Dodge will come with a new seal. These are the two most common causes of torque converter lockup. Try and slip it into neutral when you come to a stop and see if it dies. May be more of an indication of a torque converter lockup condition if it does.

there is a brake regulator on modern systems which controls the power between the front and the back breaks this maybe defective

when a car breaks most of the breaking force is placed on the front breaks as that is where most of the energy is heading so the car sinks down. if the same amount of breaking force is placed on the back wheels as they rise they have less friction as the weight is forward so they will lock up.
the device is designed to maintain more force to the front, if it fails the system will apply even force to all wheels.

recommend cosulting a certifed garage or local dealership about this problem.
Warning; continual driving with defctive breaks is illegal and may result in injury or loss.

Check axle seals for seepage. Also wheel cyls. If drums are old, they may be too thin and becoming "egg shaped" which will also cause lockup. You need to check all three items to find your problem. To check drum thickness have any brake shop measure inside diameter with an inside micrometer The min diameter is stamped into the brake drum on the outside edge.

Probably a bad torque converter lock up solenoid...

Try starting it in neutral, and putting it in drive without your foot on the brake (I know the car will take off in quite a hurry if it doesn't stall but it's an easy way to check for this)

If it doesn't stall, apply the brakes, and if it stalls then, it definitely is a bad lockup.

I don't know if you're familiar with the torque converter function/operation, but where it is a fluid (liquid) and not solid coupling with the engine, lockup is used at certain road speeds/engine RPMs to get rid of the power loss that always occurs between the pump and the turbine of the torque converter. It mechanically (through transmission oil pressure) locks both parts of the converter together so it then acts like the engine crankshaft is bolted right to the input shaft of the automatic transmission.

But, as you might imagine, this system has to unlock the converter when you apply the brakes for the same reason applying brakes without the clutch on a manual transmission stalls the engine.

Bad lockup solenoid will cause this to happen... The converter stays in lockup and as soon as you try to stop the vehicle, you also stop (stall) the engine.

It also might be something else but I'd say I'm about 90% sure on this one.

calipers stiff moving or slide bolts seized in the bore