In reverse when trying to accelerate car shakes

You were 100% correct. I actually have three out of the four motor mounts are completely gone, as you can seeing my pictures. The new transmission mount beside the bad one. The one we pulled out is in two pieces. The same with the front motor mount, and the passenger side mount has no rubber left in it at all. My motor was actually rubbing on the steel engine cradle. When I put it in reverse the motor rolled up so far that the passenger side trans-axle pulled out of the transmission and just bouncing around. Hence the very loud rapping noise, and severe vibrations. Also the car would not move because only 1 trans-axle was connected to the transmission. So replacing the three bad motor mounts brought the engine up about four inches, trans-axle popped back into place which solved all my problems. Car drives like a champ now. Thanks very much for your assistance in what I thought was going to be a $5,000.00 transmission job. It ended up costing me $70.00 for all four mounts, three hours laying up under my $500.00 car. Turns out I got the better deal after all. Sincerely, 1HappyMan.