Yeah the AI is ridiculously hard to get right. I spent more time on that than anything else and it still sucks! I had checkpoints for the CPU racers to aim for, skip them if they pass them and logic to avoid obstacles, reverse and back up if they hit the terrain, but when those conflict they get confused. I have a new-found respect for developers of racing games.
I used physics based driving, so the pivot should be the same as a standard front-wheel drive car.