The clues to your answer lie within your own situation. I know, sometimes it'd difficult to read our own sitches when we're in the middle of them, but your wife has very clearly responded to one approach, and totally CAKE-ATE to a second approach.
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One week later she moved in with him.For the first few weeks I didn't pursue her at all, didn't call, text, email. Then she reached out.
vs.
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I'm running out of options and patience. I love her so much and there is nothing else in the world I would want more than be together and have a happy marriage again. She knows that and that's why she plays the "waiting game".
I think you lost your way with the "I will love you no matter what" part. It's okay to WANT to be with our spouses, but to actually NEED them, and to be willing to put up with "no matter what" from them smacks of enmeshment and co-dependency.
I'd strongly advise that you go back to what clearly WORKED. Go dark (having no kids is the PERFECT opportunity to do so), be mysterious, aloof, and "act as if" you are moving on with your life -- without her.
I don't suspect it will take long for her to come running. When she does, COME HERE FIRST before responding to her, and we can help you handle it better this time.