Should I Just Leave My Mum?

im 16 yers old and hiv a 10 year old wee sis. I help my mum do house work ( dishes,hoover,polish,clean hamster and rabbit cage) but she always says i do nothing. My wee sis is 10 years old and after shes eating she just leaves her plate sitting there and never puts it away in sink. she comes in from school and just throws her bag and jacket on floor so i ask her to pick them up and put them away but she just goes 'Naw, dae it yirself', speaking slang. i grab her and tell her to do it but she digs her nails into my arms, kick and shouts at me then does a pretend cry to my mum coz i gently hurt her back. my mum starts shouting at me and telling me to **** off sometimes. then ive got to clean up my sis plates and sweetie rappers coz my mum says 'Shes only 10'. i get really angry coz thats no excuse at all! then mum starts shouting again at me...again. she tells me to piss of and go and get a job when she knows ive tried. ive also applies for college in august. my mum doesnt work and never has so she doesnt know how hard it is now to get one. my sis constantly using abusive words towards me and mum does nothing to sort it out. she only says ' shes only 10' and thinks its cute. my bro moved out when he was 17 ( now 21) to live with my gran and he still is. My bro tries to sort katie out but my mum and gran shout at him aswell. my wee sis get let of soooo damn much and i cant take it anymore. so am i just better living with my other gran coz this home is sooo depressing.