My folks have had many Grand Cherokees, including their current '05 and '07 models. I've driven them all, and they are *very* solid on the road, dry, wet, snow, anything.

Those mechanics are wrong... if her Jeep is "fishtailing" there's something wrong. That's not normal no matter what's in the diff. The diff, tires, road... something is broken. What tires are on it?

If you're willing to help, take a drive with her. Preferably on the same roads she travels... see if you can find exactly where it happened. Oil, sand on the road?