Will someone please help me get through to my little sister?

I am 13 years old. My sister is 9. She acts like she's 4. I'm really worried about her. My mother buys her junk food and ice cream. My sister eats the stuff all the time with my mother and at meal times she probably eats twice as much as I do. Her face still looks like a toddler's face - loaded with baby fat. I feel like my mother doesn't want her to grow up. She delayed getting her a bra ( and she desperately needed one) until my sister came home crying. My mom didn't tell me about my period until a couple of years ago when I got it and started crying because I thought I was injured. She hasn't said anything to me about boys yet (thank god). My mother is always babying my sister - she makes her get animal balloons whenever we go to amusement parks. My father is wonderful with everything, but my mom has no job so she is around much more. My little sister is a horrible wretch whenever I am near her. She gets mad over the simplest, stupidest things. She gets mad whenever I say ANYTHING it doesn't matter what it is. She threw a fit when I called her smart ( and I was not being sarcastic). Her face drops whenever I enter a room. The worst part is that my mother never tells her that she is wrong. My mother is always taking her side, bringing her up to her room, and asking me to stop haring my sister. I am really worried about her; I'm afraid that she will develop health problems and die before me even though I am older. I'm even scared that she might die before one of my parents. She is an extremely smart little girl who knows how to get what she wants and play the victim. I always get yelled at because my brother (he's 11) won't say anything. My mother always points out that if I had a legitimate point, why doesn't it bother my brother? My sister seems to think that I'm trying to be her mother. I have to ask her if she's really hungry every time before she eats something. I'm very worried. I can't do any shopping for us because I can't drive to the closest store - I'm only 13. My mom is the only one who has time to do shopping because my dad is a director of buildings and operations at a college. I think that my mother is trying to convince my sister that I am evil. She constantly criticizes me. My sister will not listen to me. When my parents go out and leave me in charge she tells me that I am not the boss of her. I can't get her to stop eating. She has only one friend as far as I can tell and that friend only shows up because of our luxurious house. I know because she's always watching TV on a big screen or staring at the chandelier and hardly ever talks to anyone. I mentioned this to my father and he said that it's good for her to have a friend. My sister thinks that I think that I know everything. I know that I don't know everything. There is a wedge driven between us. She yzes everything I say to find an insult and throws a tantrum if she can manufacture one. I care about her - she is my sister after all. When I grow up I want her to be around. I don't want my kids asking what happened to my sister in all the photos of my childhood. I don't want to tell them she died of a heart attack at age 15. My little sister is scaring me. I don't know what to do with her. I can't use logic with her because whatever I say has a filter that goes through her ears to make it seem insulting. She won't believe that I'm trying to help her and she thinks that I'm trying to pick fights.