she may forgive you, but the marriage is changed forever, and she may well never want you back. And in a way, why should she? You cant take back that you shagged someone else. You had your fun. Perhaps she needs to see if the grass is greener too before she decides whether she wants you back.
Sounds to me like you thought you had found something better. Did the other woman not want you? why should your wife want you back under those circumstances? The fall back, when it didnt work out with the OW?
You need to do a lot of work on yourself to understand why you felt entitled to fuck someone else, to put your sexual gratification above your promises to the marriage. Dont go blaming her for any of it - if there were problems in the marriage why didnt you talk about them rather than look elsewhere? If you start finger pointing and saying 'its because you didnt x,y, z' then you are not going to get anywhere. You need to own your own decisions and get to the bottom of why you made them. You need to give her as much space as she needs - even if that is for ever, and keep your contact solely to do with the kids. Dont harrange her or try to get her into conversations, dont doorstep her, dont invade her space. You chose to walk out, so have the respect to stay out. You need to understand that what she does now is actually none of your business, and in many ways you need to get on with your life with the thought that she wont take you back, and that she is free to make herself a new life.
IF she wants to go to counselling it may turn out to be about how to split up for good. It may be about how to move forward together. If it gets to that point then it needs both people to be happy. Maybe she wont be. Maybe, when you hear what she says, you wont be. You are both free to make those decisions.
Why did you tell her about the affair - was she at the point of finding out? Was the other woman going to tell her? Or did you feel too guilty and uncomfortable with yourself keeping the secret? Or was it because you had a new set up ready to move in to.
And BTW, paying maintanance, seeing your sons and not hassling her are the minimum you should be doing anyway - you shouldnt be looking for some kind of pat on the back for not being even more of an arsehole now she has rightfully refused to take you back.