Boyfriend's Female Best Friend

So my boyfriend has two people he calls his best friend. One is a guy who I'm fine with, but the other is a girl. They've had feelings for each other off and on before we got together, but every time one of them is in a dedicated relationship they stop talking or hanging out. She's standoffish around me but he says that's just how she is. And her little sister (who's like 15) sees my boyfriend (19) as her older brother. The little sister is a sweetheart, and I don't want to do anything to take away my boyfriend from her, but I don't trust the older sister.

I've been with my boyfriend a year and a half and in all that time him and his "best friend" have barely spoken, and when they do he later tells me she was rude or didn't really seem to care. But he still says she's his best friend. She's been dating someone about a year as well.

Anyway, she just got sworn in to the Air Force, so I've encouraged him to try and reconcile the friendship, going against my own wishes because I don't want him to ever think I stopped their friendship and blame me for it. But they have a past; they dated for a week and broke up because it got too awkward, but over time they've both told each other they had feelings for each other at points where the other was dating someone. They spent the night together and cuddled and watched movies but didn't kiss (because she had a boyfriend at the time 😒) and afterward he told me about how attractive and how sexy he thought she was. And then later he said he felt bad for ever going over there and regretted the whole night.

They've had such a weird but also such a long-lasting friendship that I can't decide if it's my place to encourage or discourage the two being friends while he's with me. As I said he's barely spoken to her and she's barely spoken to him since we got together, but I don't want to be blamed for that, and at the same time it makes me so much more suspicious.

Am I overthinking this or overcomplicating it? What would you do?