The cars should be raised up first by about a wheels height and a half before having the wheel attached, and then drop down when the wheel is placed. Currently the car gets kinda annoyed when attaching a wheel (starts making ground scrubbing noises while the car stays "stanced").
Sometimes when you've placed the wheel into it's space and get in the driver's seat, the car jiggles in place until you start driving. This can sometimes harm the player.

Or something like that until proper car servicing mechanics come into play. This would just be an OK workaround IMO.