Ex's flavor of the month. Kids involved. HELP!

I have an issue with my ex husband (the father of my 2 children) introducing the kids to his latest flings. The first time was right after we divorced and the kids (2 and 3 at the time) started throwing HUGE tantrums every time it was time to go to dad's. He informs me that they've been spending a lot of time with this girl he's "interested in". I asked to meet her and she REFUSED. She even tried to go into my kids daycare and have "conferences" with the directors who also happened to be my bosses. They eventually stopped seeing each other and the kids behaviors improved instantly. About a year later my kids tell me "we had a sleepover at ___s house". Come to find out it was some girl their dad was sleeping with and he was dragging them along. She moved out of state about a month later. A few weeks ago he tells me he wants to bring the girl he's been seeing for a few weeks to have lunch at the kids school! (They're now 4 and 5) I put my foot down and let him know that was unacceptable. (He then decided she was more important than lunch with his kids) I'm tired of him introducing the kids to every girl he sleeps with and I'm afraid of what it's doing to them since he clearly doesn't put their needs first. Do I have any legal rights here? I don't trust these girls or his judgement!