rear end shifting while driving straight?

This sounds like you have a rear bearing hub locking up or one the suspension trailing arms is broken/loose. I would raise the rear of the car and rotate the wheels to see if there are any noises and that the wheels rotate smoothly. Also, check the tire themselves to see if the one of the tires is coming apart which you should be able to see while spinning the wheels. Then use a flashlight to inspect the suspension parts. Please go over this guide to help jack the car up safety:

https://www.2carpros.com/articles/jack-up-and-lift-your-car-safely

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