I completely agree with what Steve and Sandi said above. Actually, before reading Sandi's post, I was going to say something in the same lines.
First, you do need to take more responsibilities in your household due to your wife's leaving. You want to give your kids the best you can give them (whatever that is). Your kids should be your primary focus. A big part of DBing is making sure your family (yourself included) are taken care of as much as possible. The yourself part is the GAL part. Just like you need to take care of your kids, you need to take care of you, regardless where this situation ends up. So, the choice is not between detaching and DBing or between DBing and fighting for your marriage.
DBing is about surrendering control of your marriage. Respecting the fact that your W is and independent person entitled to make her choices, even if you disagree, even if you think they are harmful (more about that later). DBing is also about you being an independent person making your choices that is capable of living a fulfilling life with or without her.
Myself, I got to a situation where (we had been living nominally together for a while back then) I was ready to pack my things and go or let my W go on a 24 hours notice. I had my life (at least the basics) figured out. I had a plan where I would want to live, what I wanted to do, how I would spend my time with my kids etc. It never got there, but it gave me the peace of mind and confidence to live my life as I saw fit. It allowed me not to pay attention to the things my W did when I disagreed with them.
DBing is not hoping for reconciliation. DBing is simply being ready when it happens, and also being ready when it does not happen. Hoping for reconciliation is IMO the opposite of detaching. It would be much easier for you if your mindset is something in these lines: "We will be better off if we R, but I am perfectly fine if we do not. If she wants to R, I would be open to work on it given the right circumstances, if we find out we still want the same things".
Second, why do you want to know if your W had an affair? Think very seriously what you hope to accomplish with acquiring that knowledge? IMO, you will only get hurt. You want your W to come back and commit to your R, not look for excuses what she had done. From what I had already read, she would need awful lot of excuses for what you already know. IMO, if she ever wants to come back to you, you need to discuss what happened this time, and how you will avoid it from happening again. If she does not want to come back to you, what she has done should be left to her own conscience. Simply forgive her and move on.
Knowing she had an affair will simply turn you into a victim in your own eyes, and you will need redemption. Do your kids really need to go through that too? It is much better that you forgive her and focus on either R or moving on.
Third, I think what Sandi is saying here is that your W rejects your judgement and your opinion. She left because she currently wants to be independent and make her own decision. She did not ask you whether to move out, right? So, what do you think you will accomplish by telling her what to do and what not to do? Most likely, you will only justify her decision in her own head.
You can judge her. I certainly do judge her (and I do not know her) just reading your posts. But your judgement should stay for you only. You cannot judge her in front of her, her friends, relatives, and certainly in front of the kids.
Nobody here denies that not spending time with one's kids is bad parenting. However, you need to understand and respect that you do not know how she sees things, what she is going through now. She denied you that right. She may be seeing things in different perspective. Maybe she needs to go through something (therapy, MLC ...) before she could feel she can be a good mother. Maybe, that is how she internally justifies her behavior. I honestly, cannot think what may be more important than spending an afternoon with your kids after you have not seen them for weeks, but that is not the point. The point is she denied you the right to control that. She claims to be the only person to make that decision, and you need to respect that.
That does not mean that you cannot tell her in a non-judgmental non-confrontation non-controlling way that she needs to spend more time with your sons. If you want to send the message, you can doing by saying that "our sons will be very happy if you spend time with them today / take them to dinner" or "they miss you" . You can try such friendly / positive suggestions and see if she would be willing to respond.
Of course, if you need to protect / defend your sons, you can do that. If she harms them one way or another, you need to do something about it. But this would be a unilateral action. You will not find her cooperation by shaming her. That is what Sandi probably meant.
