Considering your daughters' track records.. stealing, acting out.. etc. I can see why your divorcing spouse doesn't want them at home without adult supervision. Went you went away, didn't one of your daughter's throw a party at your place?
It's perfectly reasonable for them to go with their mom or stay at a friend's house. Heck.. that's part of single parenting.
You have plans, commitments set well in advance. Define your boundaries without rancor and go from there. You can't control what your divorcing spouse says. Just know what you do is based on what is right, not righteous.