The current system, from what I gather, calculates the player's and the vehicles movement to get the relative movement of the two and thus the damage. I say an easy way to fix the annoying hop-in-a-car-and-die thing would be to have whatever calculates the damage to check to see if the vehicle is moving. If it is, then proceed normally with checking the damage and such, but if it is not, then ignore the player's movement completely. It should work.
