Q: vibration and smoke from tail pipe

Check for diagnostic trouble codes. If the smoke is blue, oil is getting into the combustion chambers and perhaps the rough running is due to partly fouled plugs. If the smoke is black, the air fuel ratio is way off and you should use a scan tool to look at short and long term fuel trim; if out of range, that has to be diagnosed and the underlying cause repaired. It is always possible to have multiple causes of rough running and vibration at idle. While stationary, switch from drive to neutral. If the vibrating lessens, the engine’s motor mounts could be faulty. Other causes of vibration are a faulty harmonic balancer. If these initial checks do not reveal a cause, if you were to request a diagnostic from YourMechanic, the protocol is pretty standard: a certified mechanic will test for ignition, fuel system, air induction and/or engine sensor problems and these possibilities are tested, in a sequence, using a diagnostic "decision tree". Often, the problem is limited and straightforward, that is easily repairable. There is a good chance of that so I recommend that you request a rough running diagnostic and the responding certified mechanic will travel right to your location and get this diagnosed and resolved for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic.