The short is that she will limit discussions with my BIL but she is nit interested in working on iur relationship.
Rather ironic that the cheater is laying out the ground rules for the spouse who has been betrayed. She can toot the trust word at you all she wants, but she is the untrustworthy spouse, not you. Don't forget it. She will flip this around and try to make it appear as though you have violated her privacy by snooping and now she can't trust you. Do not allow her to play that game.
Since her lover is your sister's husband, it makes this whole situation very critical. It could destroy the entire family's relationship. Let's say that your W and brother-in-law run off together, maybe get married (I have actually seen this happen in a family). They will be gone and you and your sister will continue being siblings. When your sister finds out........and she will find out.........the first thing she will ask you is, "Did you know"?
Did the DB coach tell you what to do when your sister faces you, wanting to know why you would not tell her? Are you prepared to keep this secret from her and your parents for the rest of your life?
I am not a fan of exposure, but I do make rare exceptions....like when it is within a family, and the WW has no intentions of working on her M. First of all, your W and brother-in-law should not see or talk to each other. An affair has to end abruptly and go cold turkey (there are no closures for affairs or tapering off). She has basically told you to suck it up b/c she's going to continue contacting him. She has the audacity to tell you that you'll just have to trust the affair is over! So, every time the family meets for dinner, you will be subjected to sitting there and make nice while they make eyes at each other?
Did your coach tell you how to deal with those types of situations?
Have you seen or talked to BIL since you discovered the affair? Does he know that you know? He should be scared sh'tless that his W will find out........or scared of you! If he thinks you are going to be a good little boy while he plays with your W, he will make your life hell.
You need to think this through very carefully, before you decide what action to take. Do not warn your W of anything you are thinking, or anything you may do. Tell her nothing. Let her wonder what you are thinking. (I have a feeling she's not very worried, based on what she told you about her continuing to talk to OM).
I think it will boil down to you having a choice to make in where you place your loyalties, and what "doing the right thing" would mean to you.
To your knowledge, has your sister's H ever cheated on her in the past? Has your own W ever had an inappropriate contact with the opposite sex in the past?
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!