Interesting to note that on the paper it says that she can meet him in five years. This means that for two years after his murder, she hadn't been looking into this sort of stuff even though it wouldn't have been that hard for her.
I'll bet you that she suffered in similar ways to what MC's mom has suffered (remember, she chose to move them all to a remote house the grandmother owned), people mistreating her for the actions of her family in this case her rapist father. Heck, it was probably the family that took her in for awhile that did the mistreatment and instilled into her a sense that it was her fault. This will probably be explored through her being bullied and all, but I'm guessing she wanted to meet the MC to try to give him a 'little sister' again, to try to atone for what her father took from him in a way.
Some of her more secretive actions are probably also the result of trauma. She saw her father being murdered by the MC, I imagine that her general hesitation and reluctance to talk with him and even running away from him on sight at the grave were due to a PTSD like response from watching the murder. Might even be making her want to hide who her dad is if she's afraid that MC might kill her too (even if just unconsciously). She both wants to help the MC and support him but is deep down scared of him, and probably seeing him at two of his lowest points (begging her to kill him and the massive anxiety attack in the restaurant) have probably bolstered her sense of needing to help him which is why she's more openly approaching and talking to him.