shakey towing of jeep cherokee

I've owned Jeeps for over 40 years. Sounds like it's definitely a death wobble. It's not as common on Cherokees as on Wranglers, but it happens. It's usually caused by worn bushings, worn tie rod ends or draglink ends, or some of each. Basically, when these parts get worn, even a little bit, there is enough looseness in the front end that death wobble occurs. There should be videos showing how to check a of these components. Otherwise, go to a good four wheel drive shop - dealers almost never have the experience to diagnose or fix this problem. I generally have to replace the bushings In the upper and lower control arms every 40,000 miles or so, and rebuil the tie bar and drag link ends every 50,000 to 60,000 miles. The reason for your Death wobble can be hard to find unless you know what to look for, but it's usually not too hard to fix.