How to deal with wife who moves OM in with our kids

I'm trying to decide how to speak to my children (two girls aged 3 and 6) about STBXW and OM. I feel my wife deeply betrayed me and my family. My details are in another thread but I want to focus on the OM moving in situation and get some advice. Several weeks after D-Day, my wife and I were "bird-nesting" our kids (we took turns watching them at our place). Wife botched the separation talk with the girls and said "Mommy and Daddy do not love each other any more" and "Mommy has a new boyfriend". She proceeded to introduce our girls to him a few times after that. I was very upset about all of this - I thought it was too fast and too soon. The real blow was when I soon left for 2 months to return to my home country (to regain my sanity and be with family and friends) and my wife moves OM in three days after I left. She said she told me "he'd be staying there" and that I agreed to it. Hell no. She claims that due to his job he is only there a few nights a week. For me that's a few night too many. I'm trying to handle this as best I can. I'm very angry about it but there's not much I can do about it at this point. I returned and have a new place to live (my plan all along) and she is moving out soon as well. I told my oldest girl (6 years old) that I wasn't going into the old apartment because I do not like OM. Just looking for some guidance with regards to the kids. I feel I am in the right that wife has behaved extremely inexcusably.

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