Is she okay with the kids knowing? I might say that as well, and you're being honest here when you spell that all out, something like: "Look, it's not just me being "selfish" here and keeping you from what you want out of spite. What are the kids going to think about you cavorting around with a lover? I'm not going to lie to them and cover for you, and you're putting your wants ahead of any concerns for not just me but our family."
From a child's point of view, I think this is a valid concern- what will the kids' think? But if she was concerned about what the kids will think, she wouldn't consider it. Also, the concept of infidelity may not be relevant to the kids at their age. It's an adult situation and beyond a child's comprehension. Kids might learn a rated G version of the 10 Commandments but a simplified form. What their mother does with another partner- they aren't going to see it or hopefully not be told about it.
As a child and teen, what I thought about my BPD mother was formed through her behavior at home. What was confusing is that it was normalized. For kids, their home is their example of "normal". As an older child/teen I could see that my friends' mothers didn't act like that, but we kids didn't have a say about BPD mother's behavior.
A parent's relationship with a child is formed on how a parent relates to them, not what that parent does with anyone else. I don't know if BPD mother ever had an affair or not but that would not have made a difference to what we thought of her as kids, or teens, compared to our relationship with her.
Kids also learn from both parents. If you want your kids to learn about monogomy, then you would need to role model that for them. While you can't control your wife's choices, you can hold on to your own moral code. One possible reason she may want you to agree to an open marriage is that, if you do, and you do it yourself- then it may avoid shame for her, after all if what she's doing isn't OK, you doing it might make it OK. If you think it's not OK for her than it needs to be not OK for you.
One option is to say to her "I understand you want an open marriage and I don't. I wish that you didn't want to date other people but I also can't control your decisions. On my part, I will remain monogomous. I've said all I can about this topic and don't wish to discuss it further".
Then you walk away from this, the decision is up to her now. Don't say what you would do if she did have an affair. She knows how you feel. Let her think things over.


