shakey towing of jeep cherokee

If it was mine I would take the Cherokee to a good alignment shop and have them align the vehicle with as much positive castor as could be adjusted into the front suspension regardless of specifications. The condition you are experiencing is called "Bump Steer" and is caused by the front steering not being dampened by pressure from the power steering system and to little castor. Castor is the main alignment setting that affects steering stability thus the more castor the more the front wheels will tend to remain straight instead of oscillating back and forth.