I haven't seen this issue addressed yet

I have an '04 330i with factory sport suspension. It currently has 115,000 miles on it. Recently when I am driving around a corner (lets say a 70 degree turn) the back end feels like my tires are tilting like they are loose, but they aren't. I have had it looked at and I was told my shocks need to be replaced, but I don't think that is what is causing this problem. It isn't a constant feeling, instead, it jerks like my back end wants to break loose 2-3 times through the turn. It is really hard to describe, but I am not driving it fast, in fact, I am only going 25-30 mph. What would cause this?

Make a right turn and the weight shifts to the left side of the car. If you have no dampening, or reduced dampening from dead shocks, you will experience what you describe. Driving in a straight line spreads the weight across all four wheels, so you probably won't notice it as much.

If you have the original rear trailing arm bushings in the car, they too could be worn and contributing to your problem.

RTABs, bad shocks, or possibly a torn subframe, but that`s a long shot....

Rear shock mounts are a known weak point. Replace them along with your rear shocks, they're inexpensive.

Someone swapped your BMW for an old Alfa!

How do your tires look? How much maintenance has your suspension had throughout the life of the car? If your tires are "scalopped", you probably do need shocks- at least..