1. If your wife isn't cheating, then you will have an easier go at this.
2. That being said, it sounds like she's cheating. The ILYBINILWY speech usually means she is in love with someone else OR she wants to be soon. It means that though you may be a good provider and father, you aren't the LOVER/PARTNER that she wants. And if she doesn't already have a new boyfriend, she's going to get one soon. She's putting her romantic happiness above the well-being of your children. That's what ILYBIMINWY speech REALLY means.
3. DO NOT MOVE OUT YOUR HOUSE. Why should you move if SHE's the one who wants to end the marriage? This also will work against you in custody hearings if you get a divorce. Let her get her own flat. She needs to feel consequences for her actions. Why are YOU paying the consequences for her decision to leave you. If she's leaving you, she needs to be doing the leaving. Let HER leave. Why should you leave?
4. Go see a divorce lawyer immediately. This doesn't mean you are going to file. It's to know your rights, and also to get advice on what not to do (like move out of your own home).
5. Give her space, work on yourself. Get some exercise and some hobbies. She needs to know that you are ready to move on IF SHE LEAVES.