First off I’d get a big car. Shoot any and all exteriors of the car. I seriously doubt that you can shoot anything other than a close-up with the camera in the car so I would remove the windshield, cut a large hole in the roof for lighting access (and possibly shooting), roll all of the windows down, get a door mount, a hood mount, tow it all on a genny equipped car hauler, drive down the road and shoot away. I presume that you will be shooting this production to a track playback and not recording it live.
Good luck,
Ken
P.S. How did you get such a job if you had no idea of how to shoot it?