When stopped, the car shakes violently and feels as though it's about to shut down. The battery is new, A/C compressor was just recently replaced along with a motor mount. Had a tune up two days ago. The car has a great deal of trouble accelerating, and as you can imagine, it's even worse was driving on an inclined surface.
My car has an automatic transmission.
You may have a misfiring cylinder. If the spark plug boots are getting oil on them from a leaking valve cover or you have one or more ignition coils breaking down and not firing then this can be the problem.
Have the engine scanned to see which cylinder is misfiring, and then have the coil removed for inspection of the coil, coil boot and spark plug.