I am in disbelief that you are not taking action,
Your wife told you she is in an affair - fact
OM has admitted the affair , if not in so many words - fact
Its all your fault and you are the bad guy, she will tell her family so, you destroyed the marriage, - this is what she believes - fact and this is what will be believed by all - fact
Your wife has told you she is separating from you - fact.
She is talking to the OM, BECAUSE THEY ARE STILL HAVING AN AFFAIR - fact - Do you get it.
They are planning the next steps --In January. Feb or soon thereafter Mrs. Disbelief will say she has a place to go to and OM will have a place to sleep, a bed to rest his weary body and your wife just happens to be in it. - Fact , this will happen whether you tell people the truth or not
If his wife believes he is having a platonic conversation she is a fool. - tell her so, suggest she joins another forum, say the one at marriage builders and asks for advice, this way you are on separate forums and I assure you she will be told very quickly what is happening and the steps to take.. the same as I am telling you.
So
This is sincere advice. This is hard and fast from a professional who is very successfully in rebuilding marriages, for the record not I.
While she is in contact with the OM the marriage will never recover
As of the moment the affair started you had no marriage, you have no marriage now, so do nothing and pray ,while it is good for the soul it is very ineffectual in real life or take action .
Adapt the note stating that they have both acknowledged the affair , post it on the forum if you are not sure of the words and we will help you.
At a minimum you call her family and send the note to them. She does not want to tell them because it is a secret and wants to control the message when she leaves, by sending the note now and her leaving confirms to people she has gone because of the OM. Do the same to the OM's friends, if he did not want to talk to your wife he would ignore her calls, he is in this up to his neck so pull no punches and stop doubting yourself.
They both admitted the affair to you so take action.
At all times remember your wife and the OM are pathological liars, never believe what they say to be true and drum this into your head.
Give it one more shot as I do not think you have done this.
You speak to her today, face to face, tell her the affair stops now and that she ceases all contact the OM. Tell her she is destroying two families. YOU forgive her, you will fight for your marriage and will leave no stone unturned to repair the damage and return the love between you. Together you will go to counseling to build a better and more rewarding marriage. Warn your wife if OM goes near your children you will get a restraining order against him. Say no more, present no evidence, there is no debate, look her in the eye when you talk to her.
Then
tell the family and close friends via mail, text and conversation. Talk directly with your in laws, make sure they know she and OM both admitted the affair. Do so now, Thanksgiving and Christmas are good times for her to see what she is going to miss. You must make sure you all have a great family time, she can be present or not her choice.
Carry on gathering evidence i.e. the VAR, you want to hear the innocent conversation, hide the device well.
Plan A her- for about 6 weeks, this takes you to Jan about the time she will try to leave. If she is responding to the Plan A then it goes on for a lot longer. Do not trust her carry on gathering evidence and be diligent. Do not discuss divorce or separation, it is not on your agenda, if she brings it up state it is not an option, walkout of the room.
Prepare for Plan B- if she has not divulged all and is not actively working on the marriage you start this in Jan/Feb, this occurs regardless if she leaves or not, this is when you and her tell your children mom has a boyfriend and is leaving home. She pays 50 /50 of all bills and assume her full share of the finances. Separation must be formal through the courts, call the OM as witness to the affair, see how he baulks at this.
Key for you is to get through Plan A, if she comes back to the marriage great, if not do Plan B, the effort is enormousness on your side. You will be stressed, tired and hurt all the time. If she contacts the OM at any time you are back to square one, the timescales don't change and Plan B become a reality
What ever happens you work on yourself, the children stay with you, you be firm, lead the family and show gumption, the OM is not your friend he is not better than you treat him such.
Get legal advice in readiness for a separation, follow the legal advice, she leaves she pays you to support the family, you are not having the affair she is.
The above will need some finessing but at a summary level this is what you should be working to