I think you are way too quick to take on all the blame and to idolize your wife as the spotless victim. So now she is messing around with another woman's husband all because she is just so starved for luv. Please. I'm sorry, but I don't know why that narrative is what you choose to believe. Maybe you think that, by taking all the blame, you'll have a better chance of winning her back. I doubt that will work. She'll just have less and less respect for you because she sees you don't respect yourself. Stop assuming you know all about her motivation. Of course she's crying victim and blaming you. That's her shirking responsibility.
I think you made a mistake leaving the home. That's your home too. Those are your daughters who don't have their dad home with them where they need him to be.
Wanting to forgive your wife could be a good thing. But it doesn't have to mean you condemn yourself. She messed up. That's forgivable. But you don't have to engage in a bunch of twisted thinking to justify her. That's not necessary. She got bored with her life and tried to make it more interesting by doing something not at all nice. By any chance, is she somewhat immature? That's what this sounds like to me. Her parents may be part of that problem also. I think you would have done better to stay home and tough out this whole situation. If you love her, consider going home. I think that's your only chance to save the marriage. Just walk through the door and say you are staying there. Don't do too much talking. If her texting that guy comes up, just say you are putting that behind you in the past . . . and you hope she will too.
Groveling at her feet will absolutely not make you more attractive to her. It will make you seem like you have no core, but just an inner vacuum. I'm truly am very sorry for the awful situation you are in. You're on the verge of losing so much . . . . . . but I think you bolted headlong and prematurely into making a physical separation happen. I've known marriages that survived wanton infidelity and went on to be good and strong unions. It took the partners growing up a bit. But they did it. Your wife needs to do some work on herself. Try being there for her. Talk less. Listen more. It's only been 2 weeks. Go back. Don't bring up the other guy. At some level, your wife is probably embarrassed. Some things are better NOT talked about. Don't pressure her for any explanation. Go back and act like it never happened. Maybe you'll live parallel existences for a while, not touching or being close. But give it time. You both may eventually move on and put this in the past.