I hate hearing about shit like this, unfortunately it happens all to often now days though..
Number one is you and your kids..they watch you, listen to you, model you, look up to you. love you. You going through intense pain and suffering, loosing who you thought was your best friend there are no words for.. the two of you were a team, at least you thought so, while you were busting your ass to make a better life and future for your family your partner was engaging in some teenage fantasy bullshit to satisfy her own selfish needs..
Obviously you love your wife and all she is including her faults(most) and I'm sure she loves you as well...You don't trust her and may never trust her again, that's not for you to rebuild that is for her to do..
If she is truly sorry, If she truly loves you, if she wants your marriage to survive then she is in for the fight of her life.. Counseling cannot fix that only she can... She needs to earn your trust by her actions, this will not go away, be forgotten, blow over with time... Every day she needs to wake up and think how can I earn my husbands trust back, what does he need me to do to fix this.. Yes she needs a counselor for her issues; selfishness, probably insecurities and self esteem issues as well, those are major ones for cheaters looking to fill their "void" in themselves...
Only by her actions will you trust her again.. see a counselor now not later, and if she thinks she doesn't well you need her to so she needs to get her ass in there yesterday...If you want to look at her phone, email, txt, she can't get upset.. Tell you where she is going and for how long, when leaving and going, she needs to come home when she says she will, check in frequently with you..
If you get mad then get mad, she has no right to stop that from happening or to get upset
I don't think she is willing to do all this... she seems to feel it's over and all good, water under the bridge, but you didn't violate your marriage vows she did and it's her job to rectify this..
It sucks, it hurts, I'd rather get the shit kicked out of me, but leaving now no matter how bad it is and how painful it is for you is the wrong thing to do..all you will be doing is delivering all that pain you feel to your kids....The countless nights crying themselves to sleep when you are not there, the "why is daddy leaving," "will he ever come back," "why are you getting a divorce," "I hate you both." I don't know how old they are but teens can be even worse..they have their own identity issues and throwing a divorce on top of that breeds anger, insecurity, contempt, "fuck everyone, they all leave, you can't trust anyone," Kids never ever recover from divorce, it is with them forever...It will shape their future relationships from then on..I'm sure half the members here have parents that are divorced..
All you can do is be the man you are, be the husband you are, and the father you are.. If you give an honest 100% effort you will make the right decisions, if you have to leave after then you will with no regrets... You don't need to bend over backwards, she does, if she is remorseful, and making an effort to work on your trust and marriage, doing all the things she needs to do then your part is to let her. If she is truly broken you can stand by while she heals herself and your marriage... who knows you both may be stronger for it.. Out of pain comes great strength, understanding, respect, but it takes effort on HER part not yours.... If she says I'm Ok whats your problem get over it, then she doesn't care and never will, it's over..