Your Dad sounds like he’s playing the victim and is being totally disrespectful to your Mum – not just the affair, but telling anyone who will listen about the BPD. He’s lining up the pity for when the eventual truth comes out. And it will do. There is no justification for an affair. Ever. If he’s “had to put up” with Mum’s BPD, then he should bloody well leave! The gas-lighting won’t help the BPD, for sure!
His behaviour is reckless, flaunting around town, so perhaps he wants the truth to come out. Perhaps he hasn’t the spine to leave without being thrown out.
I would be so upset to find out my children had kept the secret from me because “it was none of their business”. Of course it is! This is your family and you must be really upset and anxious.
I personally would talk to not only Dad but the OW. I would have it out with her, cards on the table, telling her you and your sister know. I would warn Dad that if he didn’t end the affair, then you expect him to tell Mum before the end of the week. He may leave, of course, but if he does he was always going to. Best now than later. If he doesn’t leave then he may tell your Mum about the affair, of course, but it seems he was always going to get caught – it’s just a matter of time and this is the point……it IS going to come out and Mum will be doubly hurt that her children said nothing nor tried to get Dad to stop the affair. Even if you don’t disclose the affair to Mum, if she finds out, she’ll know you tried hard to stop the affair. That counts.
I would line-up therapy for Mum, as someone said. She needs support anyway, besides the affair, and I’m surprised she’s not in therapy anyway.
Really horrid for you. I think Mum needs allies and love around her. It’s a very lonely place, discovering your partner has been having an affair and that others knew but did nor said nothing. It’s oddly more painful than the affair itself.