Well she's putting down conditions for you to reach out to her fam. If your BIL is cool hanging out with you, just hang out with him. She doesn't get to dictate your relationships with other people. If BIL feels uncomfortable, then that's a different issue, but it doesn't sound like that. I would just caution to not spill your beans to BIL, but hang out as friends and that's that.
About "I'm not sure how I feel" convo, I would advise against that. Of course you know how you feel - you don't want to talk to her if she's messing around. This goes back to the original NC advice that you've said to her - "we have nothing to talk about as long as you're having an affair". Hold that line and only respond or initiate anything that has to do with business stuff - like house or finances etc.
I am not sure if you need to write to her to correct what you said, but if she texts, you can just say that you have no interest in talking while there is OM, and leave it at that. Done. done.
