The Villanueva women have always been multi-dimensional characters and it's not at all surprising that Alba's sister on Jane the Virgin is the same way. When Jane was interviewing Alba for the sake of her thesis, she was surprised to discover Alba's sister, Cecilia, looks exactly like Jane herself. She asked Alba why she never mentioned they look so much alike and why Alba never really talks about her sister at all. It turns out Cecilia was the one that told Alba's future in-laws that Alba wasn't actually a virgin, which led to the outburst at her wedding that Alba revealed at the end of Season 2.
Since then, Alba and her sister had a falling out, which is why Alba refrains from talking about her at all, but Jane's curiosity couldn't help but wonder why Cecilia would try to ruin Alba's wedding. In typical Jane fashion, she turned to her writing for answers and fans got to see Jane's thought process about Cecilia come out in the form of "B—tchy Cecilia," "Horny Cecilia," and "Nun Cecilia." Through all these different iterations of her aunt, Jane realized that things between Alba and Cecilia probably weren't as black and white as she first believed. Looking at things that way, Jane correctly guessed that the real reason Cecilia tried to ruin Alba's wedding was because she was in love with Alba's fiancé, Jane's grandfather.
Surprised, Alba assumed Jane read her letters from her sister and that's how she found out the truth, but Jane hadn't. According to TV Guide, on Monday night's episode of Jane the Virgin, Alba will allow Jane to read the letters from Cecilia but only under certain conditions. What those conditions are remain to be seen, but more than likely Alba won't want Jane trying to reach out to Cecilia.
Although Jane most likely wants to read the letters for the sake of the story, there's also no doubt she wants to learn more about her grandmother's past. Jane being who she is will definitely try to reconcile the two sisters if she can, which may cause a rift between her and Alba. Jane should tread carefully with these letters; sometimes the past should just stay in the past or else it could end up causing some major family problems in the present if she isn't careful.