Is there any possibility that the vehicle came from the factory with a limited slip differential in the rear, or that some previous owner installed a limited slip differential or a locker in the rear?

If you are familiar with the corner where she says it happens most frequently, is there anything unusual about that corner? Is it off-camber, or having some sand on the road surface, or water from drainage, or anything like that?

The only experience that I've had that sounds exactle similar to that is because of my rear locker. Shortly after installing the rear locker, I broke a rear half-shaft on one side. So only one wheel was getting power. The other occasion was after I converted to a Warn full floater rear axle (with locker) and had locking hubs on the rear so I could unlock them for flat-towing the Cj7. On one occasion, one of my smarty buddies unlocked one of the rear hubs. Never noticed it on the trail (was in 4WD), but I did as soom as I put it in 2WD back on the pavement.

On both occasions, it would fishtail when the gas was either applied or removed smartly, just going straight. Apply the throttle, it would swerve in one direction; let off the throttle and it would swerve in the other direction.

That's why I asked about the LSD or locker.