Is this inappropriate?

So a couple years back, my mother-in-law started this rumor that I was upset with her because she told my boyfriend‘s ex happy birthday, when in reality that never happened. I never even knew she told the girl happy birthday, but she told people this at a family party so of course it got back to me, I Asked her why she would say something like that, when that was not true and she claimed she never said it. But multiple people had told me she did, but I let it go. Anyway, the ex hasn’t come up since then, but this last weekend we went to another family party of my boyfriends, and one of my brother-in-law‘s made a comment that he had went and got his haircut with her, the ex. And my boyfriend told him in Spanish, not to bring her up and his brother looked at him confused and said okay. My brother-in-law‘s are only 13 so he’s not making the appointments himself and I wouldn’t mind if I was aware that he was going to get his haircut with her but the fact that he brought it up on accident and then my boyfriend tried to like cover it up Made me a little suspicious. Well, it turns out all my brother-in-law‘s and my mother-in-law went to get haircuts/make up done for the party and his brothers have been going and getting haircuts with her for a minute now, my boyfriend has known this and hasn’t mentioned it to me really at all., and I told my boyfriend that I thought that was a little inappropriate for her to be keeping in contact with his ex when she knows that she had already caused drama With us when there was none before. Again, I wouldn’t care so much if it didn’t seem like it was something that was trying to be hidden from me.And that I wouldn’t be OK with my family keeping in contact with any of my exes outside of our relationship. So one I’m not sure why my boyfriend is OK with his family still being close with his ex, two his mom knows that she has already started problems with the ex in the past, but she continues to go out of her way to involve this girl in her life, and I just think it’s weird, like my mom wouldn’t do something like that to my boyfriend. Especially knowing that she normally goes to someone else when she gets hair/make up done for parties and stuff like that. It just seems strange to me and I think that if it was the other way, they were doing something like that, I wouldn’t be OK with it. Especially the fact that they tried to keep it like a secret from me was what mostly threw me off.