Before any relationship started between AM, WI, and me, I started my relationship with EL by cheating. And, though the circumstances are different from what LR describes, the response had the same structure. For the longest time, EL's husband and my wife set rules, asked questions, demanded information, and, in turn, got every kind of support we could give. Our spouses needed to know they were being heard, respected, and loved. We also spent an incredible amount of time turning each other's attention back to our respective marriages. We spent more time talking about our marriages than about anything else, for ages. We needed each other's marriages to be good - without her marriage, she's not who she is, so why would I want her to lose that?!
It took years.
The breaking of trust, the betrayal involved, was huge. My wife needed years to return to a sense of security. She needed my attention, my words, and my full focus, even as that changed and took away from my relationship with EL. (EL was engaged in the same at home, as well.) In the end, EL and I kept something resembling what we'd had, and it's grown as we've grown, but it's not what we originally wanted or dreamed of. But it IS a passionate, meaningful, amazing relationship that has lasted for ages, and our marriages ARE intact and stronger than before.
What's important is that there came a time when... the awfulness ended. The rules of how often we could see each other changed. The need for every detail to be told changed (you did what? how often? why don't you do that with me?!), especially as ... we started doing "what" and "that often" and perhaps much more, at home, as well.
There came a day when I needed a particular kind of help in my life, and WI said to me, "you should talk to EL. She'd be good for you, you need her." And we all realized that things had changed, and WI sees EL as an integral part of my life, and the affair is no longer relevant. "Oh, right, that," is now the attitude, rather than "you asshole." (It certainly helps that WI fell in love, herself... putting herself in my shoes was a big deal, for her.)
The thing is, I'm not advocating going this route. My god, it sucked. But if it's the path you're on, then I can say that it worked out for us.
One last thing: You ask how to stop smothering her with your need for attention. My answer is: insist on attention. SHE is the one who had the affair. If she wants to leave you, she should. If she wants to stay, she needs to respond to your desire for attention. She broke a promise you two had with each other, and now she needs to turn and face you and love you harder than you've ever been loved. She needs to know what you want with her, and you two need to make that happen. If she means it, that she's not leaving the guy AND wants to stay with you, she has to fulfill that desire by convincing you, again, of her love. She has to re-earn your trust. If she's pining about her guy while you're there, you can tell her you're not there to listen to that. She had an affair, she hid the emotions for that long, she can keep them private now, too - not by hiding, but out of respect for you. You need attention from her, you should get it, and it's not about her, it's about you. That's not smothering, that's keeping your marriage intact. If that's what you want, go ahead and ask for it. If she's not giving you that, she's not taking your pain and your place seriously.
Our version of this situation sucked, but it also changed my life and my marriage immeasurably for the better, in the long run. But it's been a long run, and incredibly tiring at times. Good luck.