I had this problem of my car going to the right every time I accelarate so I changed the front engine mount and right engine mount. I changed that two weeks ago and it was all normal, but the problem reappeared today. The alignment is fine along with the tire rod. Currently the car is at 172500 miles with original shocks. I revved the engine and saw no major directional movements in the engine. I don't suspect the engine mounts at all.