Family problems.

While this isn't my marriage, I have a serious conflict with my younger brother "Mike "and his choices. I was friends with "Tammy" since the age of 14. About 3 years ago I realized Tammy was a toxic person and did nothing but bring me down, she got into hardcore drugs. I ended the friendship permanently not only for this but important past reasons as well. Our whole lives she has always been the girl who uses her sexuality to get what she wants. After my first marriage with my daughters dad we had gotten into an argument Tammy and I and she decided the best way to get revenge is to try to sleep with my daughters dad. Another time she went after a different ex-boyfriend. My brother Mike has known about all the problems with her none of my family likes her because she's a toxic person and has attacked each and everyone of them personally except for Mike. Most recently Mike has been driving to visit her secretly and I most recently became public on social Internet that they were seeing each other. I simply message my brother and let him know that I do not approve and I don't think him being a part of her life is going to help his at all. And if I'm being completely honest I am really hurt because I don't understand how my brother could continue a relationship with someone he knows his hurt so many members of his family. After I confronted him he essentially told me that what he does in his spare time is not of my business which I understand is true to some extent. I have ultimately told my brother that as long as he continues to stab me in the back I will no longer be a part of his life. I can't help but feel that his sexual relationship with her is more important then the feelings of his family Maybe I'm overreacting or maybe I'm letting my feelings get in the way but I can't help but feel that this is a serious betrayal.