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I have a 2001 Coupe that tends to "wander" when driving over imperfections or rough areas on the highway. Most noticeable on speed bumps. It's like you lose control of the car for a few seconds. Everything on the car is stock.
I have the stock suspension FE1. Never had it aligned, tires look ok, only normal wear, no pulling. No accidents. First time to drive a car with wide tires and the only C5 I've ever driven. I have a toyota truck with 31's and a GMC Yukon with 16's and I have never experienced this problem.
You should have the alignment checked, and you should consider adding a little toe in front and rear. just cozzy the toe towards the maximum allowed per GM spec but don't add excessive toe.
You could also try a little more air pressure (like 1-2 PSI) and make sure all tires are at the same pressure (+/- 0.25 PSI)