have you spoken to an attorney at all? If you haven't, I would encourage you to do so (many will give a free initial consultation).
Here is why I ask. Believe me, I completely get your angst about having the kids around OW. My STBX also moved in with his OW immediately, lied to me for months about his living situation and exposed the kids to her right away. Now I get to hear my 3 year old talk about her all the time. It stinks.
However, should your situation ever start going towards divorce, (and I hope it doesn't), your H will will most likely be awarded some custody all the way up to 50% and you will have no say about where he takes them or who they hang out with unless there is something criminal going on.
You don't want to give him the opportunity in court to say that you have been keeping his son from him or alienating him. I understand that isn't what you are trying to do - but the courts have their own way of looking at things. So, if you haven't already - get some legal advice on how to avoid any potential landmines that could arise later.
FWIW - I think it's positive that he hasn't moved forward with anything legal yet. And I'm sure that drives the OW crazy and probably feed some insecurity, which may be why she tries to dictate things that happen with your kids.
