You need to realize that although it is your cousin that you probably love very much. You are still talking about a girl who has been sleeping with two guys at the same time and didn't know who the father of her kid was... It sadly is as bad as it sounds.
Jesco probably likes her but will start wondering why she slept with Jack, if it was because he did or didn't do something ? if there was more than one guy, if he can trust the fact that she won't do it in the future etc etc etc.
Given that Jesco knows that she has been sleeping around he will probably not trust her anymore, and if he says OK, he will (and if he is smart ,sorry) wouldn't go further than sleeping with her every now and then, just enough to get a serious girlfriend.
In my opinion, if I hear that a girl is sleeping around I wouldn't consider her anymore as more than a real casual stress reliever.
I lived something similar, I had a f***buddy for about 9 months, toward the end of the 9th month we started talking about maybe being more than Fb, I took a little time to make my decision, a guy I knew made a move on her, she slept with him, I heard about it. She asked me to let it go and to restart where we left of. I asked for some time (2 weeks ) to think about it, then decided to say ok.. I slept with her for the summer and at the end, broke up, and got a real girlfriend.
It may sound bad on my part but I am pretty certain I wasn't the bad guy in the story.
If I were you I would recommend your cousin to well.. find someone completely new, neither of the two, and to try to have many casual or one serious, you can't really have two boyfriend not wear condoms and not take your pill seriously...
I hope you don't take it offensively, it is the brutal (although kindly phrased) truth.
I hope it helps