I'm sorry you are hurting so badly. Now that the A has been discovered and she knows you know, your game plan may need to change. So take the weekend to feel the emotions of all of this, and when you are able, you need to decide how you want to handle things.
I will just tell you that the longer you "tolerate" her being unfaithful while she's living with you and your children, the longer it may take for her to decide what she wants. Right now, she is operating out of her emotional needs and what seems would be the easiest path to take for herself. You cannot afford to operate out of your emotions, and that is why it is so important for you to have yourself under control.
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!