BertrandRussell
"Has any child ever come to harm while in the care of an agency babysitter? No? Thought not."
I'd have thought that something bad had happened in every situation you can get unfortunately, no situation is exempt... bad things have happened to children in their parents care, with nannys, relations, step- relations, siblings, at nursery, at play groups, in schools, clubs and with au pairs.
Sadly, although these things are rare, they do happen. All we can do is use our experience, brains and our knowledge of our children and other people to keep them as safe as we can.
Unless you're saying agency babysitting is somehow exempt from real life?
OP its your decision. Don't be pushed into something you feel uncomfortable with, but equally so don't jump to conclusions about whole types of childcare without examining your decisions.
I think you sound perfectly reasonable and thoughtful about this though :) My advice is to be strong and not pushed around... in reality I might be tempted to agree with MIL then oh dear little DC has a temperature on the night/ babysitter sadly cancelled or whatever, and stay at the hotel with your child whilst they go to the restaurant.