Your post showed up twice, and I answered under the other one. I’ve moved my response here so you can see how much our responses are similar.
*** Here is my opinion, you know far more about the situation than I do and I could be wrong. But based on what you've told us, here is how I view it. If your wife was begging for your forgiveness, taking herself to therapy and doing everything possible to save your marriage, I MIGHT give her a chance (unlikely, but possible due to kids in the picture). The fact that she feels she needs time to think is, to me, an answer without actually giving an answer. She wants your stability and your devotion (you've put up with far more than most would) but doesn't really want to be married. She doesn't want you to move on - but she doesn't want to change her lifestyle. Your wife has been messed up from day one as best I can tell. During the part of your marriage that should have been "honeymoon-esque" - the early years - she was already cheating. She is clearly one of those people who needs near non-stop outside validation. The people I've known with that issue did not get past it without significant professional help - and a huge desire to do so. Those who didn't, typically blamed their behavior on those around them and have multiple marriages under their belt to show for it. Your wife appears to be the latter type. Your boys are home all the time while you are not and she is engaging in this behavior. Kids are a hundred times more perceptive than we give them credit for. My aunt is a child psychologist and she would tell you that this environment is EXTREMELY damaging to your boys. How the mother treats their father - and how he reacts to it - tells THEM how relationships work and what to expect for themselves. Kids exposed to a long term cheating spouse (even if they think they are "hiding" it have an extremely HIGH probability of becoming a cheater (I'd rather be the perpetrator than the victim) or being cheated on (find a SO just like mamma and try to "redeem" her just like you did.) Here's my recommendation. Remove yourself as a choice. You should never have been one in the first place. Show your boys that forgiveness and compassion are not the same thing as tolerating disrespect for years on end. You gave her multiple chances - she squandered them. Now, for your own health, well-being and self-respect, you are letting her go. You can still show forgiveness by not speaking ill of her to them - just say she is a flawed woman as all humans are - and you each needed different things. It REALLY helps kids if you can keep from bashing the other parent. As they get older they will have to come to terms with their own feelings and realizations about who she is and the choices she's made. Not having to "defend" her to you will allow them to process their own negative feelings. I suggest never lying about why you broke up - they are likely more aware than you think. Just keep it to the facts - "Your mom was unfaithful repeatedly. I had hoped we could work it out, but she was unable to make choices that allowed us to keep our family intact. I tried very hard to save the marriage, but was unwilling to allow myself to be continually disrespected. In every relationship forgiveness is important, none of us are perfect and there will be times you mess up too and need to seek forgiveness. But what you do after you make a bad choice says as much about who you are as the bad choice itself. Will you use the experience to become better? Or keep going down the same path? Your mom did not make the changes necessary to us to continue as husband and wife. At some point you have to choose your own happiness and well-being if the other person is unwilling to change. I reached that point with your mother." Then I'd get yourself and your buys some short term therapy to deal with what has happened. If a qualified and kind therapist can help them sort their feelings out EARLY, they stand a good chance of NOT repeating the past. You also need help. I know it is not in mena's nature to seek psychological help - particularly ex-military. There is a sense that you should just suck it up and get on with it. I highly encourage you NOT to do that. Your wife's actions and the series of events that you have been through - re-entry after enlistment is REALLY, REALLY hard. Pain when not dealt with well becomes suffering. But suffering is NOT necessary. Pain is there to tell us to look at the problem and DEAL with it. To do something different. I would suggest a male counselor who has experience dealing with infidelity (like the man that runs this site.) Your wife is, in my opinion, a very, very, very bad bet. She has a track record - and is ambivalent about even trying again. You deserve far more. And your boys deserve to see you remove yourself from a unhealthy situation, take time alone to heal yourself and reset how you apporach relationships - and then later find a woman who treats you with love and respect. Then they will have a role model of what reltionships SHOULD look like. I am sorry that your wife's issues have hurt you - you deserved to come home to a woman who could give you an environment to heal within. That she actually hurt you further is beyond disappointing and sad.
BS - Female
Married 27 years, one adult child DD May 2016 “When we are no longer able to change a situation, we are challenged to change ourselves.” - V Frankl