Run this experiment.
1. Go to U-haul, and rent the 2 wheel (front wheels off) trailer.
See if it does the same.
If it does, disconnect the rear drive shaft and see what it does.
If it is stable with drive shaft disconnected and U haul lifting front wheels off the ground, you ruled out a misalignment, weak hitch, etc.
2. Now try towing without the U haul and front wheels on ground and ditto rear.
See if the problem recurs.
If it does, try disconnecting the front drive shaft and see if it recurs.
Off hand, I think you got it on 4wd and both axles are locked... and that is the source of the problem.
The front wheels are not freewheeling nor are the rear --- and it is 4 wheels fighting each other via the center diff.
If I am right, there should be abnormal tire wear or rapid tire wear on towing.