My car vibrate when I come to a stop...have car in drive with the brake on....

About a year ago a mechanic working under my car told me the transmission mount moved...when put into gear there as a slight movement visible when viewed from below...he had the car on the rack as he pointed it out. The vibration stop when car is put into neutral.
OK that needs fixing...
Is that the cause of vibration? or could the engine mounts be wearing out.
Car has 134,000 miles on it.
NOTE: I have switched from Premium gas which is recommended to regular...switched about two months ago.

Sounds like bad motor mounts. Try checking your mileage - I think you'll find premium gas is a bargain.