pop your hood start the car put the e brake on, now shift it from park to reverse, while watching the engine or stand out side have some one else shift it for you.

if the motor jumps hard and moves a lot the mounts are shot.

also look at your dog bones, are they straight or twisted a bit, like the engine is not straight anymore.

bad mount can cause vibrations in park or driving.

sounds like you need a new axle too, that wont have anything to do with a vibration in park, only when driving.