Hello and welcome.
Does it seem that the engine is running fine?
When going from drive to park to reverse, does the vibration change?
Sounds like an engine mout or a transmission mouunt.
While driving, the engine is torquing, and therefore taking the load of different mounts than when in reverse. Best way tom check is to place in drive, foot firmly on the brake, and hit the gas-then release. Have someone looking at the engine to look for excessive movement of the engine. do the dame in reverse.
The front/upper (pasenger side) is pretty common, as is the "dogbone" on the front lower of the engine. If while doing this, the noise changes, or is different between inegine torquing in drive and reverse, then it is definatley a mount. Just need to look at them, and figure out which one. there are also trans. mounts thaty can do the same thing, but will need to be viewed from underneith.
It depends on the mount. The lower dogbone is approx. $45 plus 1 hour labor.
The front/upper is approx. $150 plus 1 1/2 hours labor.
Trans mounts range from approx. $75 to $175 with higher labor costs.