Well, unless she is totally dumb and clueless she probably would resent being disliked, and would probably by now have given up trying to get her parents to like her. I doubt she'd be much interested in making friends with the new sister, especially if it's that obvious the new sister is preferred over her. She'd be more likely to actively try to hurt the sister.
This story has indeed been done many many times, so you need to make it stand out somehow. More interesting than the girl just being disliked and unwanted would be why nobody likes her. The wonderful person who is disliked for reasons having nothing to do with anything they are or do is cliche. More interesting would be the character who is disliked because there isn't any reason to like her. Maybe she didn't something terrible to her family a long time ago. Maybe she lies. Maybe she's just such a bore nobody can stand to have her around.