1990 cherokee shakes badly only at 50-55mph

You make no mention that you have had a fault code scan run, do that first.

How old are the good tires? These speeds usually mean belt or balance problem with tires...If new tires, they need to be re-checked for balance...and not out of round...also check for bent wheel...due to chuckhole? Sometimes a bent steel wheel can be hammered straight...hope this helps.

This can be a tie-rod end popping or a ball-joint rocking in its socket. A tie-rod end is not hard to replace, but there are a few tricks to use to avoid really messing up your front-end alignment. The ball-joints require more tools to replace them and they are heavier parts requiring stronger tools.

Both of these jobs are the type done by a Front-end Alignment shop. Evaluating how bad the parts are takes experience unless the parts have shifted out of their mounts.

Noise is a minor symptom of the problem. Excess tire wear is another, as well as vehicle shaking, wandering, hard steering, or failure for the steering wheel to smoothly return to center after a turn.

The Autoparts stores have loaner tools to use for free to replace these parts. A front-end alignment is recommended even if the repair went smoothly. Can't emphasize enough that air powered tools are used to disassemble some ball-joint parts. Loaner tools are often what is used AFTER the part is reached after using air tools.

REbalance tires.

Many things will cause vibrations, especially on 4WD trucks. Causes include: worn ball joints, worn tie rod ends, bent wheels, tires out of balance/shifted belt in tire, worn steering dampener, worn u-joints, worn CV joints, engine problems such as engine misfire, a bad fuel injector clogged fuel filter or injectors, worn ignition parts, etc. I suggest you apply the service brake in gear and give it a lot of throttle (power-brake)to determine if the engine is running smoothly or if it runs rough. Also, with the hood up, you can see the shaking if it occurs. If rough, check everything over and repair as necessary. If smooth, start checking ALL other vehicle systems and repair as necessary.

Check to see if you do not hava a buckled wheel or a badly loose wheel bearing. Jack up the front wheels and spin and shake them. There should not be any play or wheels running out of true.
Have the whole front suspension checked out, it could be any one or a number of things contributing to the shaking.

Did you have your tires balanced? It could be a piece of mud or snow stuck to a tire rim. Also, check: tie rods, ball joints, struts, wheel bearings.

Quite possibly I would start there get tires checked

you are apply torque to the engine upon pushing on the gas pedal so the law of nature states the engine mount maybe broken

you have a warped rotor which is causing ball joint.tie rod end.idler arm(if equipd) probs.bad rotor caused by sticking caliper which over heated and warped rotor.and also bad tire or wheel or both.put the wheel on a balancer and see if its bent or if tire has belt blister.replace rotor,caliper,wheel bearings and ball joint and any other loose or worn susp/steering gear.if you just replce rotor , going to happen again but worse damage.poss breaking pwr brake booster from vibration. gino R