Great idea! It reminded me of a remote-controlled car I had when I was a child that worked the same way—one button moved it forward in a straight line, and the other button moved it backward while turning. I really liked the idea; congratulations on the game and your effort!
As for the controls, I have some reservations. I think the car loses its direction when you release the reverse button, and it keeps sliding backward as if it were on an icy track, for example. Another issue with reversing is that when you start reversing, the car takes a moment to begin turning. I think having it start turning immediately when reversing would make the controls more responsive.