You have two options:
Option 1: Plan your life so that you don't have to eat in the car. I have a friend that only allows water.
Option 2: CLEAN YOUR CAR! You can eat in the car, but...vacuum it every now and then. My DH is fastidious about this. He leaves nothing in the car. He doesn't allow the kids to leave anything in the car. It works wonders. We eat in the car, but every scrap of paper, cups, etc, exit when we do.
So pick one. Your family will adapt either way.