There's a lot of overlap between people with BPD and people who have been sexually abused. As far as I know, there's no known causation, but I'm just adding that to the discussion.
I would not assume she's lying. False rape accusations that are actually proven false and not people who have been pressured to recant, are statistically miniscule.
I think transference is a possibility; I mean, I could have been your grandpa, which is why it's coming up now in the aftermath of his death. He could have been a supportive figure to her otherwise (many abusers set themselves up this way so that persistent contact with the victim seems normal), and so she's transferring because she's unable to reconcile the two images of him in her head. I mean, this is all guesswork, I'm just saying, it could be transference from someone who isn't you.
Especially, I mean, you've said yourself you do regularly touch your family in their restricted areas (even if it's just their bum) as a Funny Thing that you do and if one of her trauma responses is to be uncomfortable with touch, especially in sensitive areas, especially by men, then you have been unwittingly triggering her for a number of years.
The first thing I would communicate with her, is: I don't remember touching your vagina, but I do touch people's butts and now understand that that is something you are not comfortable with and is upsetting for you. I'm sorry, I didn't know that, and I won't do it any more. I can't know what happened back then now, because I can't remember, but I'm sorry for anything inappropriate that may have happened on my part. None of it would have been done with sexual or malicious intent.
I think that completely outside of this, you absolutely need to stop touching your family members bums, like that's not a normal thing to do and doesn't sound reciprocal so why, I mean you're already known as the Cousin Who Will Keep Touching My Bum to the rest of your family and you're apparently okay with that being Your Thing. Why.
Anyway, back to the topic: I think you need to meet her - and I think having a mediator there would be a good idea. I'm not suggesting this for the IF YOU MEET HER ALONE SHE'LL LIE EVEN MORE BRO but because such a meeting for her, while she considers you her abuser, is going to be incredibly intense and hard. It's probably not going to be easy for you either. Having a supportive figure there (and don't pick someone who you feel is 'on your side' because that's not fair to her) would be a really good idea. A therapist - someone with professional knowledge - would be even better.
I think she definitely needs to see someone - for her BPD then she definitely needs a psychiatrist, but what I think would be really good is if you were to contact her - perhaps second hand through your mum, as that's how she's chosen to get in touch with you - and suggest a meeting between the two of you with a therapist.
I do kind of think that a second revelation is due, of perhaps worse abuse by someone else. I also think that by admitting you don't remember she will get very upset, but if you maintain that you're trying to be honest with her then she should come to accept it hopefully.
In the interest of disclosure, I experienced very similar CSA from another (unrelated) child, at the same age as her. I have never attempted contact with them, because I'm fairly certain that they were being sexually abused by an adult themselves at the time, and I don't know whether there would be satisfaction for me in contacting them about it, as they will have their own pain. I already attempted telling my parents age 14, and was called a liar. That was devastating and although I have touch issues myself, the main trauma I have felt from that has come from being dismissed and condemned by my parents. Please don't do the same to her.
From my personal experience, what I have wanted most is to be believed. Also, I have interacted with other CSA survivors through the internet and real life, again, a few with BPD. Being believed is also often a major point with them, because the stereotype of BPD is an unstable, inconsistent unreliable person.
This is probably incredibly long, sorry about that. I'm going to post this and then delete my name from it; I check some people's post histories and then end up feeling weird that this information is available to someone who's been looking up a frivolous comment on FFA or something. However, I will be checking back if you have a question or response or something.