96 avenger shakes at red lights

Hi guys. I bought an avenger that runs a little rough and I am trying to figure out if I have a fuel and air problem or a broken motor mount. In neutral or any other gear the car does not shake. In drive it shakes horrendously. Watching the engine as the car is put in drive the engine moves towards you a about 3 or so inches. Now with throttling the car takes a while to accelerate even after I stomp it on the highway to merge. On home roads I can let off the gas and the car will sustain itself at 25 to 30 mph. 1st gear is not very responsive. All other gears seem to be ok with acceleration. I am trying to find a good starting point. Advice? Comment with any needed info

Also the accelerator has a twitchy feeling where it will move up and down as if the car is trying to drive itself.

It should never move that much. Sounds like broken mounts to start. Have you started with plugs and wires?

Seeing as how there may be multiple problems involved my recommendation would be to pull the spark plugs and run a compression test.
This should determine whether or not a serious top end issue exists which could make everything else a moot point.