You're driving an e30, right? +1 on the shot subframe mounts.
If they're OK, you're probably feeling the notorious BMW 'twitch.' Don't head into a corner too hot...brake before you get into the turn, then gradually feed her more gas as you go through. If you let off the gas in the turn, or worse use the brakes, you unload the rear suspension and transfer weight to the front. When you hit the gas again, the camber changes on the rear tires break them free, and the very light rear end starts chasing the heavy front end.
I lose traction around almost every 90deg turn...and I have an LSD! That's what makes these cars so charming...dexterity!