Lookup "Jeep Death Wobble"
^^^ This.
Basically, it's tire balance.
I have experienced true death wobble twice. The first time was in a 1999 Jeep Grand Cherokee V8, the same series as the 2001. They have a solid front axle, so what often happens is one front tire gets out of balance, and the shimmy or wobble gets transmitted to the opposite front wheel and sets that one off. If the conditions are just right (or just wrong), the two tires set up a harmonic such that each oscillation reinforces the wobble on the opposite side.
Checking the tie rod ends and track bar is recommended. Despite innumerable claims on the Internet, worn/loose tie rod ends and track bar ends cannot CAUSE death wobble, but if they are worn they are less able to dampen transmission of wobble from one side to the other side. Simply rotating the tires may help ... but it could also make things worse. The real cure is to be certain that the tires are balanced correctly. The trick is how to do that. Most shops today have equipment that's much smarter than the people who run it, so they get lazy and don't pay attention. Sometimes a Jeep with death wobble needs to be rebalanced three or four times before somebody finally gets it right. "Close" is not good enough.
At 97,000 miles, if they drive like most people and grind the steering wheel with the vehicle not moving when parking, it's probably a safe bet that the tie rod ends are in need of replacement.