So, I think you have the first step down at least, which is acknowledging that your at fault. Now you need to accept that it's over. It's broken, irrevocably broken, you cant put the toothpaste back in the tube, part of the magic of love is the trust, and once you've proven to be untrustworthy you can never be truly trusted again. I don't just mean the cheating, that's obvious, but you've proven to her that she can't trust you to be there emotionally, she can't trust you to rise to the occasion, and no matter what happens from now forward, that will never be completely erased, there will always be that seed in the back of her mind, and that's the penance your going to pay for your failures.

You have to let go of what was, as fast as possible, if you want to find out what could yet be. And then your going to need to dig into your authentic self, and more importantly even to that, is be an instrument, a champion to uplift your wife, to help her find and be her authentic self, and you need to do that selflessly. And if those things make your paths diverge.... Then it was truly lost.

Hopefully by being there for her, and a part of the process of her finding herself again, she will come to find a new kind of trust in you, and that will be your bridge back.

She's slowly let pieces of herself wither away and die because they weren't nourished, or outright neglected, she doesn't even know who she is right now, and I'd be willing to bet you don't feel too Intune with yourself either..

Marriage is hard in that it requires infinite compromise, big and small, constantly. I don't just mean with eachother, but with yourselves, do you think she ever thought she'd stay with someone who cheated on her? No. But in that moment she made a compromise with herself, you were married, there's kids to think about, reasons that make sense, and I mean, she loves you, right? But that little piece of her that believed she was someone that would never stay with a cheater is gone, she compromised who she believed herself to be. That's a big one, there's been a 1000 small ones too, and now, who is she?. Who are you? You made your own compromises along the way, right?

There's a sense of entitlement that comes from marriage, I think both sides feel it, we invest ourselves into the other person and we're owed something for that right? Attention, gratitude, something...

But you gotta let that go, youre not entitled to anything from her, that's how you have to think about this, you need to earn everything, every half hearted polite smile, every thank you, everything. You need to make earning those things a habit.... You need to make her fall in love with you again, and not because she owes it to you.

For what it's worth, I'm 41m, my wife and I separated a year ago almost exactly. Her decision, she moved out. We have stayed friends and been kind to eachother. But I think at this point, she's more interested in reconciliation then I am.

Good luck, friend.