What do I do about my mum and sister..?

My sister is so horrible to me but never gets any consequences. She spread horrible rumours about me around our school, I told my mum and she did nothing about it. I went to her crying because people were being horrible to me because of what my little sister had said yet she did nothing about it besides tell her to tell her friends it's not true? She tells me things like 'you need to loose weight' 'you should eat that you should eat this because you're too fat' (I'm average weight for my age) and then turns around and slaps me (in front of my mum) and my mum still does nothing about it.. The thing is though, if I was to do anything like this to my sister, I would get grounded for months on the spot. I tried asking my mum if I could move in with my dad as I have GCSE's this year and I don't want my sister distracting me because it upsets me how she gets away with putting me down all the time yet she told me to 'fu*k off' ? I HATE living here, I love been bullied in the past but now it feels like my own little sister is bullying me? But if I retaliate I will get punished really badly and she gets nothing. What do I do? I've had enough of it.