Engine vibrates very bad when cold 2.4 single

The best ideea is to scan your Engine Control Module (ECM) with a diagnosis scantool connected to the Data Link Connector (DLC) of the car. You will find definitely the engine fault code - "P...." and the clear description of the error(s). Also you can try to erase this error(s) from the Engine Control Module (ECM) memory. If errors are "sporadic" type you certain have permission to erase them, also for some kinds of "static" errors.
If you don't have any diagnosis tool, you can also try something else. For check up if the engine have a proper turn, you can successively disconnect each spark plug coil from the engine wiring system, engine idle, car stationary. When you operating this you must be free of chassis ground (battery ground)!!! When you disconnect a spark plug coil and the engine speed (rpm) drops, that means this coil works properly. When one coil disconnected and engine speed (rpm) still remain unaltered, this coil (or spark plug) is out of order. First you can change only the spark plug and check up again. If no changes the coil is defective and must be replaced!
My recommendation is first to change all spark plugs on the engine, and after that check up coils.