Oh no, that sounds so, so hard I don't really have any advice, maybe someone with more experience of a spouse in an open affair will. It's true that you can't stop your H from telling your kids about the OW, or from introducing them.
I think I would calmly tell your H about the emotional issues that your 13 year old is having and that they are in a fragile state. You could even approach it in a problem solving manner: what can WE as parents do to help your kid. It might not work but if you are careful not to attach any blame in this matter (underneath any denial he KNOWS what he's doing is affecting the kids, you don't need to tell him) then maybe he might step back from this very selfish step. In a way it might be easier for your kids to know about the existence of the OW, because it might explain this very messy situation a bit more. But honestly, a 13 year old is old enough to make up their own mind about whether they meet the OW or not, and all you have to do is support the decision. I have left my kids to decide for themselves whether they visit H in his flat or not, I will facilitate it if they want to but increasingly they don't want to.
