RE: sleepover, tough one. We didn't have visitation and staying at WH's place set up for at least a half year because of many reasons. But then they did start every other weekend. I hated the idea of it. I cried non-stop the whole first weekend. But ironically, it was good for them. They needed to know that their Dad still loved them, that he still cared about them. Before going they felt bad for me, and said they didn't want to go, but I put on a big smile and sent them off.
One of the hardest things I've done (and this whole MLC is very very hard!). But you know what happened? THEY felt better after doing it. It actually helped THEIR self-esteem. For me it sucked, but for the kids, it was the right thing to do. (Though they tried to protect my feelings by not telling me they liked it for some time still, but they did!)
I had heard that if you push the H away too far from the kids, they may eventually just move on too much. Which means they will not be there to love their kids through the important stages, be there with them enough, financially support them, etc. Now, it's really partly a personality thing, but I sort of instinctually thought that it would be harder for me and the kids if their Dad moved too far from their lives. Does that make sense? So what could I do that was in the best interests of the kids?
So, I guess as far as a sleepover goes, it wouldn't really be bad for them to try one, and see how it goes.
However he should probably NOT have OW there. All the parenting advice goes against that.
I dont' remember from your sitch, have they had sleepovers with just your H? Would he consider a sleepover without OW?