It would be awfully nice if Grandma didn't have to ask for a towel before she dared sit down on a seat, and if I didn't have to worry about burning my legs on the exposed seat-warmer wires. But then I think about all of the things I would have to give up if I got a new car.
The first thing I did when I had kids of my own was tell them, "Never, ever try to make a bed. It can't be done." And because I believe in leading by example, I only make mine when people come over and insist on looking at it.
After any valiant effort to clean the car, I enforce strict rules. I announce that the dog is no longer allowed in the main area of the van, and whatever the kids bring in the van, they must bring out.
I'm a real stickler. For a few days. Then my kids break me.
Keep in mind one of my favorite ideas: We're not raising children; we're raising adults. While it may be easier in the short term to just clean up after your daughter, it's very important that she develop the sense of responsibility that comes from knowing she can sort out her own messes.