I know you have tried speaking to your mum alone and she says she agrees, but have you tried getting your mum, dad and sister sitting down at the table and talking about it as a family.
It might help your parents understand how you're feeling and that you don't think it's very fair how you're expected to be in debt to try and help your paretns when your younger sister isn't paying her own way. Your parents aren't going to be around forever and sooner or later your sister will have to pay her own way. Personally I feel the sooner the better as she will gain some independance.
I'm not saying you're parents shouldn't give you or her money occassionally but the fact you're expected to pay your way and she doesn't does seem very unfair.
Try writing down what you're feeling so that when it comes to talking about it together you know what you want to say and don't forget anything. Don't let your tempers rise as this will probably end in a screaming match and you won't get anywhere. If you feel yourself getting annoyed, call a break and take 5 minutes away and go back clearer minded.
Have you tried looking into a shared accomadation? You have your own room but you share the living room, kitchen and bathroom and pay rent sometimes the rent includes bills other times it doesn't.
Sorry my reply is long winded but I hope this is able to help you in some way.
Good luck