I need advice for dealing with friend and BIL

My old coworker/friend, let’s call her Sarah, started having a fling with my brother in law a year ago. She tells me she sees other people, is sexual with at least one, and says my BIL would be “perfect” if he would just “grow up”. My BIL is no prize. He is cool but he really does need to grow up and get his priorities straight.

IMO, Sarah kinda used BIL as a rebound last year, then found something new. She still talks and sees him, but she’s never going to settle down with him. I think she just really likes the attention when she’s bored.

BIL is IN LOVE with this girl. He follows her around like a lost puppy. He cant keep his hands off her, which she does not return the touching in public, but she doesn’t really stop it. It makes him looks creepy and everyone in the room gets uncomfortable.

This weekend we had a party and I invited her. She came and BIL goes into his weird lover boy mode and it’s annoying. Sarah leaves after a few hours to go see a band. BIL is devastated she left. Texting furiously on his phone. I assume she said he’s welcome to go see the band because a half hour later he leaves the party, where all his friends are and goes to join her. He was just in love struck mode saying “I have to go man, I have to go”.

There is a lot of history with it being awkward with me being friends with her and him being so creepy.

So I need advice. I feel like I can’t invite her over when he is around. Even tho they do hang out on their own, my husband and I can’t stand his behavior around her. Should I say something to her like “hey you’re really messing with my BIL life by hanging around him and not being interested in being exclusive.” Or should I just stop being around their interactions? That would mean I don’t invite her to group events, but then he might and I would have to say I’m not cool with it if he asks.

I’ve tried to talk sense into BIL but it’s pointless. He’s possessive of her and makes it seems like I try to interfere with their relationship when in reality he is the one who feel in love with my friend.