Generation/cultural gap

I just don't know what students are thinking actually. The students I teach are the kind of lower banding students (not so academically talented). Some of them come to study at this school because they still have got a sort of vague hope that they can go to university. However, after nearly a year, some of them have just given up.
Recently, that student called Vivian really gave me a lot of troubles. Her English is good, but her attitude is shitty. I had never bothered much to chase her for her homework. But things are getting worse. She's become a pain in the ass. She stirs up a sort of "hidden" feeling of hatred among her friends towards me. They gave me suspicious look or behave nastily in my lessons. I have enough of all these. I have to discipline her. And by chance she's one of the head prefect. How wonderful for her shitty behaviours and being a head prefect at the same time!!
To be honest, I don't like to punish students. I think they are mature enough to be dealt with. But not so. It's getting more and more difficult.