Everyone is right about lighting being the key. In a perfect world I'd have some lights set up on stands and a spot meter to "tune" the light. You can try the "white paper" idea, and also try waxed paper to diffuse the flash. The problem with the flash, though, is going to be light drop-off from front to rear when the camera is so close to the car. The back will be about a stop or more darker than the front because of the inverse square law. Since you have a tripod you can try to get around that by moving farther back and zooming in on the car, but if you have a rangefinder-type camera the flash might then not be powerful enough.
Can't recall, Ghost, did you mention the type of camera? If there's any way to mount a polarizer filter that will help a lot with daytime pics for your shots in the park.