As someone who had to use a car my nanny family owned and the first time I drove it I hit a wooden chair that was on the highway (unavoidable, couldn't change lanes and it fell off the car in front of me) I understand her not wanting to drive/use your car or hers. I had to pull over in an unsafe area with kids in the car to check for damages, call the parents, so on. We were late for where we were going, the kids were crabby and scared from the loud noise. There was minimal damage but it gave me such anxiety of how much worse it could have been.

I had a job before this where I used my own car to drive their kids. The wear and tear on my car was absolutely not worth it. Sure they paid for my gas and what not but putting on the miles and the interior being trashed wasn't worth it.

I wouldn't pressure her it could be something like either of those things. If it's the first and she doesn't feel safe or confident not driving them then you especially need to leave it alone.