You are not a mind reader. And you don't have to be. Take what your wife says at face value. I KNOW we're supposed to only believe half what they DO and none of what they say but when it comes to a reconciliation, IF it does, then listen to her words and take them at face value until if and when her actions don't match. But if she says he's out of the picture and there's no evidence to the contrary, part of the whole forgiveness thing will be to accept that and let it go. You know this.
IF you get to the point of trying, may I recommend you attend Retrovaille? It's a marriage "retreat" workshop and it's for couples in trouble. You do NOT have to be Catholic or even Christian though I'd think an atheist would not find it as helpful. Also it is free if you cannot afford it. We attended this recently so I'm positive and yet I had gotten some bad information so fwiw, that's the deal. Anyhow, we got a lot out of it. It'll give you the tools you need to help you forgive. Without forgiveness, your m is doomed. All of ours are... But your comments about your motivation are wonderful and if there's a chance for it, and for your kids sake I hope there is, be open. And be very mindful of the cynics here and elsewhere, who want to punish and "teach a lesson" to a WAS...when you hear those words remember that they are not aimed at the restoration of a healthy M, but at retribution. No one in particular but heck, you might hear yourself saying it inside, and beware of those moments. And in your Real life there will be those folks around. And I'm also not saying "try saving the M at all costs" either.
We all have to dig deep and do the soul searching to find where our boundaries are. We have to cast our pride and ego aside, and yet set and enforce healthy boundaries for ourself to protect our hearts and children's and our futures, as much as possible. No one can or should tell us what to do. Only you know, so pray for guidance AND strength and do what His will is as best you can.
Good luck, j-
M: 57 H: 60 M: 35 yrs S30,D28,D19 H off to Alaska 2006 Recon 7/07- 8/08 *2016* X = "ALASKA 2.0" GROUND HOG DAY I File D 10/16 OW DIV 2/26/2018 X marries OW 5/2016