I think the absolute first thing that needs to be established after an affair is to establish and maintain "no contact" with the affair partner. I think you should stand extremely firm on this boundary, and I think you have ground to recover as she seems intent on engineering a situation where contact is inevitable.
During a romantic affair, there is a measurable switch in brain chemistry - contact with the affair partner elicits the release of massive levels of the pleasurable and addictive brain chemicals dopamine and phenylethylamine - in far greater quantity than can be produced when in a long-term relationship. And for years after an affair or a relationship, these pathways remain. That is why you see so many affairs with past lovers or high-school boyfriends/girlfriends, or so many on-off-on-off affairs. The briefest contact can immediately stir all the same emotions and within minutes they are as strong as ever. And if she is feeling these emotions for OM, she by definition isn't feeling them for you.
Your wife claims that she has no emotional response when she sees him - you can be assured that is definitely not true. Sure she may claim he is a jerk and POS - well they say something about girls and bad boys. Every time she sees something to remind her of OM, every time she hangs out with or at places she was with him, every time his name is mentioned in conversation, and definitely every time she sees him, or hugs (!) him, I can assure you she is getting an emotional reward. And this reward is at your expense.
I have been following your story for some time and am watching her actions since your reconciliation began - first she drags you down to the same city as OM, then she ingratiates you with mutual friends of the OM, then she is hanging out with and hugging the OM, now she is saying that she should be able to hang out with OM with or without you. All the while she is showing minimal remorse, she is blameshifting towards you, she is trying to rugsweep, and most worrying, she is trying to normalize all of this. You are looking for her to put effort into restoring your marriage and relationship, but she sure seems to be directing her effort elsewhere.
So, try to step back and take an objective view of her actions, not her words. Look where this has been heading. Look where this is going. And look who is leading it there. Her affair is not over, it's on hold.
