Good answer on not discussing it on your daughter's day. If your H is expecting you to beg him to come back, why not throw a little emotional Aikido throw, and Act As If you are accepting his decision.
I don't see any reason for you to go out to eat with him and his mom next week. Arrange for him to have the kids for the weekend and you go do something fun with a girlfriend. After all, if he's going to"move on", he should get used to the reality of every other weekend child responsibilities, right?
You can say something like"divorce is not what I want, but I respect that you have made your decision. We might as well start getting used to this. I'll drop the kids off Friday night and you can drop them back here Sunday afternoon."
The more you act like you're accepting his decision, the more he'll probably second guess his decision. The sooner he has to deal with the reality of weekend childcare eating into his dating opportunities, the sooner the fantasy will wear off.
Take the high road, but make sure it doesn't look like you're sitting there crying all weekend. Let him wonder about what fun you're out having on your weekend without the kids.