It would depend on the older girl's personality as to how she would react to a baby sister. I'm assuming she probably grew up fast due to being neglected and learning how to do things for herself. I personally think she would be skeptical (rather than angry) of her parent's favortism of the new baby. But I can imagine she would also wonder what was wrong with herself that her parent's couldn't love.
Going with her being skeptical, maybe her parents have a secret about the older girl, like maybe she isn't their biological daughter and she was thrust upon them during some tragic ordeal. I'm sure you could find a way to put your own spin on that to make it unique.
Maybe the older girl already knows why her parents don't care about her and she tries to save her baby sister. Like I said before, I think it would depend on the older girl's personality and what she knows about the situation beforehand. You could also throw in a aunt/uncle that does love the older girl, but now pushes her aside for the baby. That would cause her to be much more upset since her parents have never shown her love.