Your problem may be that you have uneven braking. I worked on a car that exhibited this behavior. When the brakes were applied, the car would veer to the left and seemed very unstable. You had to counter steer to keep the car straight. I thoroughly flushed the brake lines with fresh brake fluid. It made an immediate difference. After that the car braked in a straight line even with hands off the wheel. Hope this helps.

Nolan