Scooter accident – coverage question

Hey r/insurance, hope you can help me out with this one.

Me and my girlfriend (I know, lucky me) went on vacation in Italy and rented a scooter.
The rental contract was under my name, and I asked them if they need my girlfriend’s drivers license as well because she wanted to drive too.

If only she hadn’t, because when leaving the parking lot she hit the hotel shuttles rear bumper.

Now the hotel, understandably wants us to pay right now (nearly 1000 bucks). Which we obviously don’t want to pay out of private pocket since we believe this is an insurance issue and we need to speak with them first.

Any idea about how to handle this, who is liable (us or the scooter rental because I believe they should have an insurance included in the rental (by EU Law)).

We are also wondering if it makes a difference that she was driving or that it was in the parking lot and not a public road (that’s what they are saying makes us privately liable)

Any input is appreciated