She lashed out a lot but that was only a result of how her family was treating her. Emotional neglect is also a form of abuse and can be very damaging whether the victim be an adult or child. And while the way Sylvia behaved wasn’t okay it doesn’t change the fact that she was emotionally neglected as a child and by her family no less, the only people she has to depend on for a child as young as she was. Not to mention that her parents never thought to ask why she was behaving the way she was or even checked in on her. She was always villainized by her family and never really sat down to talk about why what she did was wrong and how she could have handled her emotions better.
In my opinion the family isn't really that bad, actually they aren't bad at all. May I remind you the past Sylvia would throw tantrums and would hurt her sister but the father would only scold her a little and send her to some detention area which I may again remind you was a very nice place.
I never saw/read the brother's hurting Sylvia even though Sylvia was hurting their younger sister.
The youngest sister never took revenge and Is very kind.
Sylvia sure was neglected by her family only because she was the one who turned her back from them first, she isn't abused by them, and she also wasn't starved by them.
The bad ones in the story would be those nobles who made Sylvia that way, the nobles who compared Sylvia to her family making her hate her family.