To add to Tony's points:

1. Is this a new problem? When did it start happening?
2. I'm confused about the "wide corners" thing. Until you mentioned that, it sounded exactly like a low-voltage brown-out, which can be caused by an aging battery, or a dodgy alternator, which might affect one player more than the other. I had a problem where if I had the A/C, the heated windows and the lights on, when I hit the brake pedal (more lights), the player would brown out.
3. On the "wide corners" thing, are we talking about slow wide corners or fast wide corners? Are you pulling G's here? Do you have traction control (more electrical load)?