1. You caught your wife sexting with someone. Confronted her, she moved out of your house.
2. You are caring for your kids, more or less solo.
3. There's an OM in the picture.
4. You are trying to romance/pursue her.
5. You are afraid that upsetting your wife or having boundaries, or confronting, will set you back or have her bolt.
OK here's my advice:
1. Do the GAL activities to get some sanity so that you are not basing your happiness on whether or not your wife texts you or what mood she's in. I've been there dude. Every sentence is analyzed every tone of voice either lifts your spirits or crushes you. You are acting needy and afraid. These are all turn-offs for your wife. She can smell your desperation, which only gives her more power in this situation. In Christian terms, you have made your wife an idol.
2. Stop pursuing her. It's a turn off. It's also enabling her as a cake-eater.
3. See a Family Lawyer/Divorce Attorney right away. This is important to protect you and your kids. Know your rights, get information, learn what to document. You should, in my opinion, document evidence of your wife's affair, the time she does/doesn't spend with the kids, her move-out date, the spending of your marital assets on her new affair life-style. Hope for the best, but prepare for the worst.
4. Think through the worst-case scenario: a divorce. If that happens, ask yourself, "WHAT DO I WANT?" Complete custody of the kids, shared custody, keeping and living in your current home, etc. Think his through. IF you are caught unawares, continue to live in denial, and get dragged into a divorce, you will end up broke with the OM raising your children. If there's going to be divorce -- you set the terms. Be prepared, just in case.
5. Start talking to Starsky about setting healthy boundaries for you and the kids. You wife has got to start to feel your detachment (last resort technique) and your willingness to move on WITH or WITHOUT her (GAL and boundaries). Always being available and acting like a lap-dog won't build respect.
6. If you are being all "Christian" about romancing back your wife, think through the whole biblical counsel. You are focusing on the 70 X 7 stuff but ignoring that she isn't repenting or asking for forgiveness. You are looking at Hosea, but forgetting that he went and bought his wife back (something you can't do. Nor are you necessarily called to be an OT prophet). You are looking at the prodigal son story, but forgetting that the son has to come to his senses. You also must consider that sin (like adultery) destroys the family and the church. Nowhere in the New Testament do they advocate "nicing" a sinner into repentance or enabling them. Matthew 18 advocates an escalating form of confrontation with consequences. All the Pauline Epistles advocate "avoiding" and "handing over to Satan" an unrepentant sinner in-order to shame them in to returning to the faith and their community. People need to be made to feel the consequences of their actions. That's why it's called ex-communication. You withhold communion to wake a person up. So the practical side of Christian teaching on people like your wife is: turn up the heat. And I would argue that this is more loving that allowing a person to hurt themselves, their family, their church and their witness to the Gospel. Speak the truth in love. If you are dragging God into this, then take him seriously.
7. Get mad. It's healthy. Don't wallow in it, but it's OK to admit you are being royally screwed over. My Christian therapist once spent a whole session trying to get me mad about my wife's affair, to at least see if I had a healthy, functioning sense of self.
7. I say all this, admitting that I took the same path you are taking and made some of the same mistakes.
