First I would check the alignment, try to use a square and calipers to check if your rear axles are straight/parallel with each other. Your trying to check for toe in or toe out and if you have the back end racked one way or another. If everything checks out good and straight, i would suggest trying to remove some weight off the rear and moving it up to your DFW side. You might not have enough weight over the font wheel to hold steer.
I forgot to ask first if the rear is just moving or the hole car? If its just the rear its either miss alighment or the wheels.
Good luck
Scott