Benny,
I'm sorry you are going through this. I know just how you feel. I have been through the same.
There is something you must know with certainty that will go a long way in helping you proceed with this situation. It will help quell the emotional earthquake that is going on within you. Know this:
Your wife's affair/infidelity has NOTHING to do with YOU or YOUR MARRIAGE.
Her decision to lie, deceive, break the vows she made to you, and devastate the lives of her very children have nothing to do with you or your marriage. Infidelity is a PERSONAL problem, not a marital problem. This was a problem that existed within her long before you married. No person can "push" another into being unfaithful.
Right now I'm sure you are feeling an unbearable pain. That is normal and natural. You have been betrayed by the very one whom you invested your greatest trust in.
Do not accept any blame for this. Period.
Do not beg, plead, or bargain with her.
Now, allow yourself to become angry. You have a right to be. Be angry. But, be angry in a controlled and calculated manner and use the anger to your advantage.
Assume a cold, hard, and steely resolve toward this. Become determined that her behavior is simply and absolutely unacceptable to you or your children. Do not waiver in this resolve - not one bit. Ever.
Try to imagine yourself in the place she is mentally at right now. Deep down, she knows she has done something to you that she would NEVER want you or anyone else to do to her - ever. Deep down there is shame, guilt, insecurity, and very low self-worth. She is covering all that up with defensiveness, denial, and delusion. It is one incredible picture of ugliness that she knows she is deep into and she does not want to deal with that ugly, ugly mess.
The best way, in my experience, to get through all the denial, defensiveness, and delusion is to make the consequence for the behavior something that she cannot deny, cannot delude away, and must answer to. She is in perpetual-honeymoon fantasy-land right now and needs cold, hard reality. The best way to do that is to consult with an attorney to know your rights and then FILE for divorce and have her served with divorce papers.
Now, that does not mean you are now getting divorced. You can have it suspended or dismissed at any time. The point is for her to SEE and FEEL the real consequence of her actions and collapse her bullshit fantasy. That is at its most likely when she is holding the Petition for Dissolution of Marriage papers, with a case number, and signed by the presiding judge, in her very hands. THEN, she will not be able blame, deny, defend, or delude THAT away. That is when she is most likely to authentically come around, with actual remorse, and want to do the work to fix HERSELF, and repair the damage to her family and her marriage.
My XWW was as far gone into the bullshit fantasy as it gets. I completely detached, offered her a chance at reconciliation, and she was still in affair wonderland. It was when she found out I had filed for, and proceeded with divorce that I got the tearful requests to reconcile. I divorced her anyway and she STILL wants to reconcile. That's the power of undeniable consequences for shameful and destructive behavior. She destroyed her family. Now she must live with that.