Kyle, I think your transmission output shaft is welding itself to the center diff, or your center diff gears shims are broken or seized, causing your rear wheels to have a mind of their own.

I bet the viscous coupling is burnt out already. Take off end case, remove VC clip, remove VC, turn over and if you see the inner plastic ring has been spat out from internally, then for sure its the center diff.

Either way, I would have just removed the tranny by now. Why has it happened ? I am not sure. You have not provided enough trans info.

Of course I could be wrong, and it might just be Fred Flinstone in the back of your car with his feet down