I agree with what PM wrote, being firm but fair, and offering ZERO flex on crap like that.
Here's a story: several years ago, I jumped through hoops for awhile with XW1 with my kids while she was slobbering over OM1 - giving her whatever she wanted.
There came a time where my parents and I were taking S11 (who was S6 at the time) to a basketball game, and W said she wanted to bring OM. I said, "No. We are married, and that would not only be disrespectful to me, but to the kids as well. I have offered a quick dissolution, and you refused, so if you bring OM1, we will leave." I was very calm, and hung up.
She came and brought OM1, and I pulled S11 out of the game, and walked out. I remember literally shaking - believing I had ruined any chance at reclaiming a relationship with her, etc, etc.
She called and ranted and raved and screamed and talked about how she was taking every dime I had, and she was going to get full custody of the kids, and I was a blankety-blank blank. This went on for like a week. Then she called all sugary wanting to keep the kids an extra day to have a New Year's Eve party with OM1. I said, "No, I'm sorry, we have plans". She repeated the previous rant for about another week.
After that, our dynamic COMPLETELY shifted. I was calm, collected and in control. Every time after that, she was careful to tell me her plans on why she wanted to have the kids, and always offered a day in exchange.
Just another perspective of what sounds like a similar situation.