Sister and ex friend become close and I feel betrayed

I had a friend for over 30 years. in the last few years (maybe longer) of our friendship I felt she was getting more and more passive agressive. A few times she would meet new friends and intentionally alienate me. I could never figure out what I did to make her this way to me but I'm sure there's somthing.. Anyway a few years ago she lost her job and wanted to take a trip away and asked to visit my sister. She visited for a few weeks and I guess they became friends and they stayed in touch on FB or wherever. When my sister came out for a vacation this friend calls me to speak to her. She did this a few times with no interest in speaking with me. I was told by my sister when they made plans, that I was invited if I wanted to come.. I really felt betrayed. Maybe by both or maybe more so by my sister. At some point I told my sister how I felt. my sister,at first, tells me that they weren't really friends, that she thought she was a bit weird and their relationship was more patient/Doctor. So I said why then hang out with her if she knows it upsets me. Then she got upset and said why can't she be friends with her. I don't even know what all happened after that but fast forward to my sisters third trip back where she's still hanging out with the ex friend. I brought it up again that I still feel the same way and this time it became a real argument. She feels I'm being stupid. she said she will have to be honest to the friend and let her know that my feelings are putting a stain on things so she can no longer be friends with her. At his point I don't know anymore how I feel about their friendship. But I do know that my relationship with my sister is not what I thought. So here I am on this discussion with no questions. Just if you have any advise, I'd love to hear it.