Well, this does not sound good. What are the RPM's when it is running right vs. when it is acting up? Is the lack of acceleration present all of the time?

You may have a bad sensor, or even a bad fuel pump or clogged fuel filter / injector...
or...
perhaps the automatic trannie is staying in a top gear fully engaged when you are at idle this would account for the engine vibrating as well as poor acceleration when you take off.

Have you tried going into "neutral" when this happens to see if that would cause the symptoms to stop?

When did this all start?
Have you checked your trannie fluid level?
What fuel are you using BTW? Octane?

You may want to throw in a bottle of Chevron Techron fuel system cleaner into a 1/2 full gas tank and run the tank down. It will clean up your injectors and to some extent the sensors.