What if the client wants me to use their car while they are gone ?

If you re not comfortable driving someone else's car, then don't do it. It was very nice of the client to allow you to do so, but I wouldn't want the responsibility. Rover is not going to "cover" anything. The people's car insurance covers the car regardless of whomever is driving. That's how car insurance works. The car is covered, not the person driving.

You will find that some people here use absolutely nothing of the client's when they house sit and then clean the house when they leave. Too many potential problems if something should happen when you were using their car. Don't risk it.

If you aren't comfortable it's totally acceptable to decline the offer. They were probably trying to be nice in offering you their vehicle. I have done care before where the client has offered their car (and I've even used them on occasion) for a variety of reasons. Often it's been to save my car the dog hair, slobber, etc. that comes with a dog being in the car. I've also offered my car to sitters for my dog in the past, mostly because bully dog hairs are impossible to get out and he was a big dog. Though I also immediately thought of what Veronica mentioned was they may have wanted to ensure you had a way to get their dogs to the vet in case of an emergency. Hope this helps!

I wouldn't do this under any circumstance. You're for sure not covered if something happens to their car, and there's a huge chance they would blame you for things you didn't do (dirty car, low gas, scratches, smell). I would thank them for their generosity but say that it's your policy to not use clients things while you are caring for their pets.