Has your W told your sister there is no truth in what you say about her and BIL?
If so, then you have two options, that I see. (1) Live out the rest of your life with a woman who can't stand you, and go to family events and watch her and your BIL make knowingly glances at each other.......and making sure they don't go missing at the same time. This option won't get better, and you will live in a sexless, loveless, and lonely life. Your W and the BIL will continue to feed their affair. He feels safe b/c his poor W believes him......while you feel emotionally emasculated by your WW. (2) Physically separate from your WW. Ask your family to respect you and do not invite her to family events as long as you are separated. Set up children schedule, don't support her, and get a life without her.
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!