Mutt, I am truly sorry that you find yourself in this situation, however, there is very little to go on since you first posted back in May. To say that your current 14 posts is a "bit sparse" is an understatement.
Just a couple of observations from what I have read.
1. You twice referenced problems before you were married and then "blew them off" with an "except for" sort of reasoning.
I think those "before marriage" issues may well be a the root of the problem and you need to give us the "whole story" if we are going to be able to offer help that is potentially more "on target" for you.
2. You have been seeing an Individual Counselor. Be cautious here as some of their help is good and some of it is NOT at all centered on saving a marriage. The "thrust" of most IC is to help YOU with your problems, and from what you've said, you certainly seem to have your share of personal issues that need to be worked on. But be careful, some of the things that might be intended to "help you" can also be destructive to a marriage where "caring and sharing" are integral parts.
3. Leaving the house is an emotional reaction and not very well thought out. Basically, your "excuse" that the kids always ask for "mommy" is just an easy way for you to abandon them to an adulteress who is not thinking clearly right now, regardless of whether or not your marriage has any chance of surviving. If ANYONE should leave the house, it usually should be the unfaithful spouse, since their actions have already chosen a path of "leaving." YOUR moving out sends a message to the children that you will "cut and run" instead of fight for what is right and that you will abandon THEM. They don't understand the "reason" you have left, they just see that you have left them and their "mommy." What I sense is here is a serious deficiency of "backbone," and that may be one of the root causes of your wife's straying.
Mutt, there is no "easy" way to address adultery in a marriage. You CAN "cut and run" straight to a divorce, but you are fooling yourself if you think that is an "easy" or "painless" answer. It's not, and divorce has it's own set of problems.
Your wife has said that she loves you, but you are bouncing all over the place with NO plan. Will you "fight," or will you revert to "flight" as the answer?
4. You don't seem to understand what Emotional Needs are, and if you do, you don't understand how to, or choose not to, provide for your WIFE's emotional needs. Hence her comments to her friend in the email.
mutt, Plan A is all about improving YOU, and thereby giving your spouse a "new you" to compare. As long as you keep treating her to the "old you," why would you expect her to change?
Bottom line, mutt, is that if you truly want help and a good chance at recovering your marriage, you are going to have to start posting more and make a commitment to DO many of the things recommended NO MATTER HOW HARD THEY MAY SEEM TO YOU. They WILL seem hard, because they will require CHANGE. Change does NOT come easily to any of us, but it is necessary. The "old way" has NOT worked and has resulted in an affair. Do you WANT to continue doing things the "old way" and just "hope" for a different outcome? Or do you want to step up to the plate and FIGHT, to DO the hard things, to be a man, a father, and a husband?
Hopefully that doesn't sound to "harsh." Hopefully that will get you THINKING instead of emotionally REACTING.
Looking forward to hearing from you.
God bless.