I'll ask some questions while I humbly offer my thoughts - I hope this makes sense! Firstly - why use physics - is it to enable car bumping and the like on the track? If so, seems like a good idea to get around the problem of overlapping car sprites etc. I can't think of another reason to use the engine for this type of game.
I see no point in applying forces to the car's wheels to make the car move. In fact, I see no reason in attaching the wheels as physics objects to the car by using joints - remember, it's a viewed from above racing game, so you can manipulate the main car sprite to achieve the 'being driven' visual effect that you desire without making it too complicated to manage under the hood.
Also, rather than applying a force to the car, I would manipulate its velocity directly through events. Doing that won't kill the physics behavior but it will allow you more precise control over the car's velocity - like whether it goes where it is pointed, how quickly it rotates and appears to turn etc (so you can make it change direction on a dime or appear to slide - heading and velocity vector not the same, for example).
I have no idea why it should veer to the left like that in the example - perhaps the wheel positions are not equidistant from the car's center of mass, which causes the gentle apparent turn. I also saw that collisions between the car and the wheels were not disabled, so all sorts of strange joint fighting could be going on between the wheels and the car's body...
Just my 2 pennies' worth - hope it helps!