IMHO, you are being very controlling and you are giving him something to push against that justifies his actions in his eyes.
For instance, you told him what he was and was not ready for. You are also acting like THE parent in the R in charge of whether or not he can have a sleepover with his own child.
Your SO has moved out. You are no longer in a committed long-term R with him. He may or may not be planning to introduce the kids to his GF. You have no control over that. You can express your preference that he wait to do this until the kids have a period of transition and you tell them together about GF. But, you cannot insist on this. You cannot make his seeing the kids conditional on them not seeing GF. You have no control over that. He will do what he wants to do, and lie to you if that is what it takes to have reasonable access to his kids.
You are BOTH the children's parents. YOU are the one not ready for the kids to visit their father. But, you told him that HE wasn't ready and that the kids aren't ready. Really. Would you have had a problem if he took them out of town for a night when you were still together?
I'd suggest that you backtrack. Give him what he asked for this time and tell him that you need to set up a schedule for visitation so that everyone has clear boundaries in this area. Unless you have huge plans, I don't think a night spent with their father is going to hurt them. It hurts YOU because you want to believe that this is for sure temporary, that he's realized he's stupid, that he's already on the way home. Well, none of that is true. It may be temporary, it may not be. No doubt, after the initial pain of separation, he will enjoy having space and freedom from the dynamics that led to this situation. His relief will likely convince him he did the right thing for awhile. He is not on his way home tomorrow. Quit trying to put in stop gap measures until he comes to his senses. Accept that he has gone and you have no control over when he will return. Decide on a visitation schedule. Do not manage his R with his children. Don't put the kids in the center of this thing as a power play.
I know this has to be incredibly hard for you and that the idea of the kids visiting him just makes things feel more real. But things are what they are.
Don't worry about OW. She may well be pushing him to see the kids on his own so that he doesn't have to see you at the same time. Or, maybe she hasn't said a word. But, his leaving, the problems in the R, his need for an R with the kids, etc... are not the fault of the OW. He is making his own choices.
Also, respect yourself in all this. Don't scramble to meet his immediate demands. You weren't ready to email him. Just tell him that -- SO, I need more time to process this. This was a real surprise.
