1998 dodge caravan engine vibration at a stop

Check the wheel bearing. If over or under torqued, it may give problems. Check the drive shaft is not bent from hitting a large stone whilst moving.

Try checking for a bent rim.

Catalylic converter heat shield rattle?

Have the u-joints checked for serviceability. Check rear engine mount is in good condition check that the rear springs are still at the right height. You appear to have a harmonic vibration that is cause by worn u-joints or incorrect drive line operating angles from the angle between the rear of the gear box and the diff pinion having changed . Check the drive shaft for balance as sometimes the balance weight can throw off.

check the moter mounts..

I’m happy to help further over the phone at https://www.6ya.com/expert/jovani_c02b023fe087f6cd

if what your feeling is not an engine miss,
then it will be a motor mount,best chances are the front center one,,
or top trans mount

check the motor motor mounts for movement,
watch how far engine rocks forward or back with it running and foot on brake

check serpentine belt tenssioner

maybe because your rpm's are too low to the point that seems like its going to shut off causing vibration or possibly motor mounts may need replacing that can also cause excessive vibration

Vibrations while driving like you are describing can come from tires that have defects (internally broken belts) (wheel weights that have fallen off) or a bent rim (perhaps from another driver [not you :-) ] hitting a curb) Are the tires worn? Have they been balanced and rotated regularly? You report no vibration in the steering wheel.
Vibrations during braking can be warped rotors or discs (but this doesn't sound like your problem since these kind are usually felt in the steering wheel during braking).
If and only if you feel like you can do this safely,
you can try getting the car up to 55, placing the car in neutral, then switching the "engine off" but leave the "key on" (be warned the power steering will go out but the vehicle can still be steered though the steering wheel will be much stiffer) if you try this (do it perhaps in a vacant parking lot or on an empty road) and the vibration goes away with the engine off but while the vehicle is still moving, then the vibration is engine or transmission related. If this is the case you might hope for maybe a bad engine mount. Bad engine mounts can be diagnosed with the vehicle stopped as well. However, if the vibration remains with the van moving forward but with the engine off, the vibration is likely a problem with the tires or suspension. Try to provide some more info.
If you don't feel comfortable trying the above suggestion, please take the vehicle in to an ASE certified suspension and steering professional for further diagnosis.

Finally, I had a similar situation happen to me today. I was riding with a friend in their van and the vehicle started vibrating more and more around 55 mph. We stopped and carefully checked the front tires (including the lug nuts for tightness) but
found a tire defect. (it had several broken steel belts that caused a bulge in the tire and thus the vibration) We changed the tire and the vibration was gone. Good luck to you.