It appears I have no way of enforcing my boundary - which is that she does not communicate with the EAP while in the house, especially while I or the kids are there.
You can't stop her from communicating with him, all you can do is tell her that it is inappropriate and you will not be in a relationship with her when she is in a relationship with someone else. So what does that mean? You get to decide.
She is involved in affair fog and there is no way that she just snaps out of it.
You need to protect yourself and your child. You need to be the best DAD that you can possibly be.
Sometimes the best thing to do when you have no clue what to do is NOTHING. Sit back and close your mouth, open your eyes and ears and watch what is happening. The answers will start to come to you as you learn.