Thanks for your letter
It can be tough being the eldest in a family sometimes. It sounds as though your mum maybe relies on you too much for a lot of support in the looking after your sisters ?
Mum should not be hitting you as you say and this must stop. If she finds it difficult to cope then mum should not be taking it out on you. She should be asking for help.
Although your mum is treating you in a way that is not very nice and probably quite scary for you, I am sure that she does not hate you.
Think about trying to talk to her or writing a letter and tell her that she is making you unhappy.
If you can't do this come and talk to a ChildLine counsellor, they are here to listen and work out with you the best way to get help. Counsellors are here 24hrs 7days a week either at the end of a telephone on 0800 1111 or online for a 1-2-1 chat.
Take care
Sam