Okay I’m even more confused now.
So you asked the neighbours to help you remove a broken key in your lock - only to find there was no broken key?
So are you saying you called out the locksmith to fix your neighbour’s lock because your guest broke your key in their lock.
I would definitely send a large apology and gift to your neighbours for them being locked out of their place late at night because of your guest.
I would definitely get a picture of the broken key in your neighbour’s lock and confirmation from them that it was their property, I would still ask her to pay.
By the way always have a spare key and if you are not going to be around, you need to have a local co-host that can cover your listing who has access to spare keys.