Hi there, lei_em! Sounds like you are in a tricky situation.
I would be very careful about playing mediator. Have you heard of the Karpman Drama Triangle (
https://bpdfamily.com/content/karpman-drama-triangle)? If not, you might want to read a bit about it. It sounds very much like you'd be placing yourself in one of the points, most likely as "The Rescuer." It's not a healthy relationship dynamic and you want to avoid that. The article also has points about how to avoid being pulled in.
As for what you tell people, I wouldn't tell them he has BPD -- at least not by name. And, again, going and explaining him could be a bit triangle-isa. You say he's not diagnosed, so I'd assume he's not aware you suspect him of having it? Is he in therapy of any kind?
There may not be much you can do to ease the situation. You can be supportive and listen to them if they want to talk. Ultimately, it's their problem they need to sort out -- if at all. From the sounds of things, both of them have been going about it in an immature manner. Honestly, it sounds like your husband and his brother's girlfriend just flat-out don't get along. Not uncommon, even when there's no PD involved. Do you need to live with them for financial reasons? Is there a real problem associated with your moving out, other than drama and hurt feelings?
Also, if you don't mind my asking, what happened this weekend? Details can help get a handle on things.