Sorry I missed this. I'm not online as often as I used to be.
I think it was wrong of her to bring him without speaking to you first. It is disrespectful. Having said that, it's done now, and their is naught you can do about it. I don't think there was anything malicious in it. I suspect she just didn't thik. I would however make sure that the children know you are not only OK with their mom seeing another man, but you are happy for her. I appreciate you might have to fake the last part of that sentence. Your W will carry on spending time with the the OM and your children will come into contact with him.
I would not want my children thinking they have to hide things from me or they couldn't talk to me. Don't pry (our kids aren't spies) but let them know it's ok to talk about him in front of you.
Anyway, I like your updates Harvey. Things sound like they're going well.