If you're not open to darker opinions, I think you should skip mine.. I speak from the seat of a successful 3 party poly, live-in family.
Having forewarned you- Your wife of more than 6 years had the option of "exploring polyamory", asking for a break to date others which would give you time to find someone else and/or asking to open the relationship -before- she betrayed you. She could have respected the boundaries of your relationship, preserved your trust and honor, and made small inwards towards her needs, but at a pace that you were comfortable with..
She had an affair. She took her time making sure she was once again compatible with the ex boyfriend and had conversations with him about the two of them dating long term. Then when she knew she was secure in a 2nd relationship and had a very strong safety net in case you reacted negatively to her cheating, she tore down the last barrier to her happieness; Her guilt. She told you she cheated..
So now you have a decision to make. And I hope for your own long term happieness that, while in 1 hand you're trying to balance the needs of your wife and the other hand, the needs of your children; you make a little room for your self respect.
Sorry to shed a little rain cloud.. But I've been where are now, and didn't make room for myself.