I would do that as a babysitter so long as I knew the baby wasn't in distress. I assume you trust the babysitter to tell the difference between a baby in distress and one that is just finding it hard to settle. The only difference is that I probably wouldn't go into as much detail as your sitter - maybe just say she'd been unhappy without saying "screaming for a whole hour." That's certainly what I would prefer to hear as a parent coming home - and I would be careful not to ask to many questions in order not to get too much detail!
Yorkie, I'm completely with you. Don't understand your DH's reaction really. We've been out and come back to find one child or the other up on occaision. I was always pleased that the babysitter hadn't called. I have one gorgeous babysitter who when DD2 had an unexpected accident whilst we were out, changed her and her bedsheets and put her back to bed. She put the wet stuff in the w/machine and gave it a wash.
I think that if it was just because your DD wouldn't settle then fine. I'd hold on to her. She sounds incredibly sensible. You may end up with a babysitter who calls everytime one of your children farts. Hope your DH has calmed down today.
Sounds like you had a lovely time at the Japanese restaurant.