Will the door move with the car?(Read description)

Yes, it can move depending on how you weld it and what method you are using. For example, if you write out a program and have a GUI or press a key to open a certain door, you can make it open using that way. As long as it is not anchored when the car is moving (if it was anchored it was even then prevent the car from moving in the first place) then it should work no matter what.

It's more or less about the coding and how you go about writing your code. Hope this helps :P