I really like your plan of shutting off internet, not paying her bills, and enrolling the kids in school and daycare. What I do not like is you telling her you are about to do these things.
Also, you cannot tell her when she will have custody and not, and that she can't come to the home. Without court orders, she can stay in the house all she wants, and she can watch the kids where she is every day.
So I would suggest you do all these steps with as little notice, and thus fight, as possible. Of course she doesnt have a leg to stand on for the internet and phone - I would let her know she has until the end of the billing period to transfer her phone, and just shut off the internet now. But for the school and house, you have to be careful in how to proceed.
Its always easier to defend the status quo than to change it. So your strategy should be to gradually shift the status quo to your liking. I would not fight on the house for now, but do get the kids in school. Of course you need to inform her, but have everything set up first and ready to go. When you tell her anything, its a warning and you are starting a fight. A fight where you are trying to change something. If you just do it, its fait accompli, and she has to initiate a fight to undo it. If this turns into a court case, you want it so that she has to prove to the court that the kids are better off in her care than in school, rather than you proving that they are better off in school than her care. And that's when pulling out the 15 hour a day chat logs of hers will destroy her case.
As for confronting or threatening the OM, as a man I think that is my duty. But he's a young single idiot - you have to expect him to be laughing at you.
