1998 Ford Taurus

OK, whenever the car is first started after haven been sitting for a while, engine cold, as it may, the engine is idling extremely rough, and when it is put into gear it is still shaking pretty bad. It doesnt stop until after it has been driven for some time, or the engine has been warmed up. The car has had a complete tune up. We are debating on changing the fuel filter until we know that it is the problem. We have taken it to a mechanic who wasnt very knowledgeable, and he had to take the transmission out. He didnt do a very good job, and might have bent the driveshaft when he was reinstalling the transmission. We have recently found out that he had flushed the radiator out with Drain-o, and we had to replace the Thermostat. Could this problem be a fuel related problem or a problem with the transmission?