My opinion, after all is said and done?
Move on. You cannot control what Dad does, nor should you. He is free to live his life, as he chooses, and if he chooses to sleep with his girlfriend while your children are visiting him, then so be it. It's not like your kids are very young and not sure what is going on....your kids are VERY AWARE of how things are....they aren't stupid.
I just don't understand WHY you would want to put such a clause in your order....to me, it sounds like a nasty way of trying to control your ex's life, even when you aren't together. The kids are not being abused or mistreated....that's a huge relief, as much as you don't know it. Try being on the other side of the coin where you wonder if your kids are being beaten or fed. MUCH BIGGER CONCERN.
You're apart now....let it go. There are much bigger fish to fry, my dear.