So about 18 months ago my wife declared that she no longer wanted to married "like this". She was referring to years of control, manipulation and emotional abuse by me. She said that any physical interactions between us (intimacy) were over.
So for years you were controlling, manipulative and abusing her emotionally. And you acknowledge you were doing this. It sounds like you've stopped which is great, but here's the thing- what assurance does she have that it won't happen again, that you won't fall right back into old habits if she decides to give the M another chance? This is her dilemma. She's been through a lot and even though you've changed, she doesn't BELIEVE your changes yet. She needs TIME for that, and a lot of it. Try and have some sympathy for what she is going through.
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I begged her to get into couples counseling with me, but she said she needed to be on her own, to heal and to understand the pain she was going through and would not prioritize the marriage.
She needs to be in IC, not MC. Is she?
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I continued to work, doing the things I hadn't done for her, help with the house, the kids, the laundry, the dishes, the lunches...I wanted her to know I had changed.
This is all beta behavior and not the "change" she is looking for. It's not unusual for LBS's to do this thinking it will help, but really you're talking about being a great maid, which is cool in a healthy relationship, but obviously it's not something that's going to attract her back.
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I have tried EVERYTHING
You haven't tried the one thing that works better than anything else- TIME.
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She still presses me for a separation BUT really we don't have the means to do it.
What do you mean "presses" you? Your attitude should be that if she wants to leave then she's welcome to leave. But don't help her (or block her), it's her responsibility.
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She wants to stay with a mutual friend a few days a week, but I refuse to leave our house, mostly because I don't want to break our kids' hearts more than once.
Are you blocking her somehow? If she wants to go stay with someone then let her. But don't leave yourself.
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If she doesn't love me, THEN DIVORCE ME.
This is not a black-and-white issue. She's confused and in turmoil and you need to give her time and space to sort it out. Don't pressure her to stay, don't pressure her to leave, don't pressure her to D, don't pressure her to reconcile. REMOVE ALL PRESSURE.