Exactly what 5454real said.
Yes, you want your wife back, you want her to be able to trust you again----I get that. But what you really have to do, and this will probably be the the toughest thing, is to let go of the outcome.
You have to get better for you first. If you aren't improving to be safe for yourself, how will you be safe for her? Besides that, the affair may already have been a marriage killer, and she may not see it yet. There is a lot of processing to do. But you have to accept that, and grow from it, if it turns out to be truth.
This is coming from a guy four years out from initial discovery, but 2 years from the last D-day. But the bit of hope that I want to give you is this:
I was done in June 2011. Upon last discovery(WW is a now recovering alcoholic), I dropped her off at detox, and honestly didn't care if she ever came back home. I mean that---after 19 years of M, 15+ of it very good, I was done. Lawyered up, divided finances, and was ready to blow up everything, because the outcome had to be better than the current hell I was in.
When she did come home, I told her calmly, and with absolute clarity, that there was no change in my mind. We are finished, but you sure as hell better get working on yourself for you and your children. I was then out of the equation.
But that is exactly what she has done. To this day, she is consistently working on finding her old self, and putting her children's concerns and her recovery first---because she has to in order to stay on her path to recovery.
And I find myself still here, amazed by her committal, but still a little emotionally distant, until I feel that I am safe with her. I went from full steam ahead with divorce, to being very close to recommitting, all by actions she has done NOT to win me over, but to win herself over---to become the person she used to be....if that is ever possible.
Moral of the story---if you are more concerned of winning your spouse back than becoming the best that you can personally be, your relationship is doomed. Believe me, if you are working on yourself, she will notice. And if she wants to stay, it will be because you are making yourself a safe partner to re-engage with...not someone trying to win her over.