BTM, here's the thing... your post started off well... and then you got stuck again... do you see that^^^? Do you see where...?
Here's the thing, from where I sit. Maybe... just maybe... for the time being, you stay in the "I'm mad at my wife" state for right now. It might be a rationalization or justification, but it might be something that will help you get through the next few months. The thing to understand is, you don't have to "fix" that right now. It will still be there in the future, when you finally have time to work further on it. Other things might be a better priority, right now.
Do not act on any anger towards her. Rather, use that anger to propel you forward. Convert that anger into HOPE and UNDERSTANDING. Hope for a better future with a possible R with someone who will not lie to you, who will respect you, who will trust you. Understanding that the person whom you are currently M to is not someone you would want to be with. That you have a RIGHT to change your mind and not be with someone who would treat you that way. And belief that YOU DESERVE better... FROM SOMEONE ELSE, other than your W.
And in moving forward, forget about whether anyone else sees the TRUTH. YOU know the truth that you need to. Eventually, others may see that truth as well. Or not. But right now, they do not want to, and that is OK.
And then rebuild your R with your kids. You are their father. And whether you are M or D, your relationship with them is ONLY about them and you. They will have friends, they will have their mother, they have whatever R they will have with the OM (that is up to them), and they have YOU... their Dad. And THAT is the R you can make better, right now.
Perhaps others will disagree with me, and that's OK. I will not presume to advise you on how to handle your affairs, your M, your D, your family. This is just my opinion on how one future might look, for you...