I think you need to talk to him about having a firm fixed schedule and no changes and he shouldn't discuss schedule with her first but with you. If he wants the time for his family, then he should be upfront and honest about it. His behavior puts both you and your daughter in a bad position.
Somewhere around 11 both sks started to see more of the reality of their situation and made some interesting observations. I think that, without bashing him, you can say, "I understand that your dad was not honest with you and that you feel guilty if you would rather do something else. I would like to work with you to make these transitions easier on you." or something.
If you know he lied about being off, then I think she deserved to know that upfront. That's also no way to get her to bond with her stepmother - by lying about spending time with her. He shouldn't sell his child an incorrect bill of goods. That will only backfire for everybody.
Personally, I really hate split Christmas, even if I understand it. It is so much nicer on Thanksgiving when the kids are either here or they aren't and everyone can relax. Maybe it's time to put schedules in writing and stick to it.