Well, to be honest if you're defensive about the actual idea being criticized, I think it means that at some level you know what a massive cliché this is. Which doesn't mean that it can't be turned on its head or freshened and reused in some way. I think the key is why the older girl is so disliked by her parents and why they favour the baby more. That will also influence the interaction between the two.
Like RoxStar said, she wouldn't have much reason to like sister or bond with her.