On the way to New York, Tom insists that he and Gatsby switch cars. Along the say, he stops at Wilson's garage for gas. He even taunts Wilson with the yellow car (as Wilson has repeatedly asked to buy a car off of Tom).
After the climax of the novel, in which Gatsby tells Tom that Daisy doesn't love him anymore, Daisy runs out of the Plaza Hotel to Gatsby's car, insisting that she drive her home. Even though Gatsby has the girl, Tom feels he has won the war for Daisy. He drives Nick and Jordan back to the Eggs.
Wilson knows his wife is cheating on him. Myrtle, knowing this, runs out to meet Tom on the road, thinking that the yellow car is Tom's. Daisy runs her over and then speeds away.
So, here's the breakdown again:
To New York:
Tom drives Gatsby's car
To the Eggs:
Daisy drives Gatsby's car