If an engine is getting to much fuel it will usually stall out right after starting or won't start at all and have a Strong Odor of Gas.
Is your engine light on? If so have codes pulled write them down and post here in forum.
The engine shake can be cause by missfiring, Vacuum Leaks, Bad Engine Mounts.
Usually with a Bad or Failing Fuel Pressure Regulator the engine will take longer to start. Ex: the vehicle starts right up = good pressure regulator. Engine turns over for 10 - 15 seconds before starts = Bad or Failing pressure regulator.
Watch the video at link below for test with test equipment....