Who is responsible?

I have just had a massive argument with my parents regarding who’s responsibility this is because my sister is going on a camping weekend with her rainbow guides group this weekend and I’ve been invited along as a volunteer.
Our parents don’t think that little sister will manage on her own because she is shy so finds it hard to make new friends so parents want me to look after her whilst on camp and that includes; tucking her into bed and reading a story to her, making sure she brushes her teeth and eats enough, interacts with other girls and making sure she is dressed appropriately for the different weather conditions. However, I think that a) that is a lot of responsibility on me and, b) the other girls may either be jealous or want as much support from me as sister is getting.