1. I won't be telling the other wife. There are a few reasons for this: a) She is blissfully unaware. Loads of people have affairs and the cheated partner never has a clue that it happened, and carry on living their happy life. In some ways I wish I was one of those, but I know I would have found out or suspected by now so am glad it is out in the open. But I don't want to blow up her life for something that might never become a problem for her.
Your wife might not be the first woman with which other betrayed spouse's (OBS) husband has cheated. They might've had a Dday in the past but she thinks they're reconciled or in the process of reconciling.
But if she doesn't know about any prior infidelities, she might notice that her husband seems less interested and more disengaged from her. She might've already noticed that he's preoccupied with his phone and spending a lot of time on social media. She might be really uncomfortable with his reignited "friendship" with your wife, but he's lying to her and gaslighting her brain into Swiss cheese to convince her that nothing's wrong. Worse yet, maybe she caught gonorrhea and he's convinced her it must've been from a toilet seat.
Therefore, your assumption that OBS is "blissfully unaware" might be inaccurate; more importantly, it's self-serving. You're deceiving yourself into thinking that you're doing OBS a favor, when in reality, you're afraid of an ugly confrontation and you're terrified that your wife will leave you if her boyfriend's wife finds out.
b) This one will sound crazy to a lot of you but again, if my wife went behind my back I would never know. Her honesty has made this a better situation than it could have been. So to betray that honesty isn't something I want to do. It would be me going behind her back when at no point has she gone behind mine.
This is willfully naive. As I said in a previous post, if your wife is comfortable with OM lying to his wife and participating in his betrayal of her, then she's comfortable lying to and betraying you. Maybe she won't lie to you about when she sees him and the fact that she's having sex with him, but she's probably lying about using condoms with him (they're both clean and monogamous, so what do they have to worry about, right? ) I can already tell you with 99.99% certainty that she's lying about their relationship being "just sex" because the OM is an ex.
I also take issue with your characterization of her "honesty." When she initially started talking to him, she said it was just as friends and that you had nothing to worry about. She then escalated to an emotional affair... before blindsiding you with her intentions to make the affair physical.
2. I won't be giving an ultimatum (at this point anyway). One of the things I love about my wife is her determination. She has achieved a lot in her life and telling her she can't do something is not the way to get her to stop. She needs to WANT to stop. Read on on this one though.
Translation: Your wife is a very selfish and self-centered person who would never let anyone or anything get in the way of fulfilling her desires. I'm sure that this isn't the first time in 15 years that she has put her wants and needs over yours; this is the just the latest and most egregious example.
But sadly, you think that your wife is the higher-value partner in your marriage... despite the fact that she and your mutual friends would characterize you as the "perfect husband." Sadder still, your wife knows you feel this way, which is why she's so confident that she can wipe her feet on your heart.
But while I don't begrudge her to this point, I reserve the right to change my mind and I am not happy about this. She said don't make me cut it off yet, and I said you need to do what you need to do, but know that this is hurting me more than I have ever been hurt, and way more than I thought was going to be the case when I gave my "blessing".
You've already changed your mind; your wife knows this and she doesn't give a shit. Besides, if hurting you was enough in and of itself to make her stop, she could've never brought herself to put you through this hell in the first place.
Also, if you think you have some kind of advantage over this guy because she's married to you and you have kids, think again. I speak from experience when I say that having an ex as a romantic rival is probably the most disadvantageous position you can be in. They have history and maybe even some emotionally "unfinished business." Their memories of each other are tied to a younger, more carefree time in their lives, before the day-to-day drudgery of bills, kids, household chores. I'm sure she even remembers their fights fondly, as they probably didn't involve the more mundane matters that you squabble about as a married couple.
My first marriage ended when my ex reconnected with an ex-girlfriend and was unwilling to cut it off, even though it was destroying me. I had already forgiven him for an affair with a co-worker, who he was much more indifferent about, but I knew by the way he spoke to his ex and the look in his eyes when he fought about her that I had no chance. I didn't want to file, but it was my only way out of infidelity.
So to conclude, if you're going to continue on your current path-- which is to do nothing and hope the affair fizzles out on its own-- the only advice I can give you is this:
Wear condoms every time you have sex with your wife and avoid ejaculating inside of her, if possible.
The first reason is you need to keep yourself safe from STDs, since you are no longer in a monogamous relationship and you have no idea what diseases this guy has and who else he's sleeping with.
The second reason is that now would be a terrible time to have another child because of the stress it would add to your marriage and make it more difficult for you to leave. Also, if she were to become pregnant in the near future, at least you would know with near certainty that the child isn't yours.