i don't know about the shake for sure, but i am betting that the chaeck engine light is going to be a miss fired cylinder.very common on chevy.get it checked as soon as possible.
The engine mount (which are made of rubber) are worn out.
You have a serious problem. Have your car looked at before you drive it.
If it is running fine at high revs the most likely problem is an injector
You may have a broken engine or transmission mount.
possibly loose?? or engine runnability problem. Alos drivetrain vibration or wheel balance problem will cause it
Water in fuel? Have vehicle scanned to determine the problem
Replace engine cushions
The Vehicle shakes because of the virbration produced by the engine at the stop sing
engine rubber mounts or timin out
That's a misfire-ah....
Engine miss.
Have vehicle scanned to determine the problem