Tom's advice looks very good to me. I'd add to it, though, lift the
car's rear end and check the rear wheels for fore-and-aft play. You're
looking for play in the rear A-arm bushings, mostly. It's one of several
things that can cause your symptoms. Just personally, I'd suspect a toe
change is occurring on the rear suspension.
Tom's point that this is a dangerous problem is most well-taken.