hugs x it is no wonder your emotions are so mixed up , mine were too when my abuser my mothers second husband died a couple of years ago. i too am distant from my family, like you i both hate and care about my family. i have found being distant is best for me, i still have contact through cards on birthdays and christmas with those of my extended family who do care about me, but have no contact with my close/nuclear family. i too was concerned for my younger sister when i left home, tried phoning her regularly, but over time she chose to break contact. as long as you give your sister the opportunity to have a relationship with you either by phone computer or whatever, there is little you can do as the choice is hers in the end. i have got to a place within myself where i believe as long as my sis is happy without me in her life then that is ok with me, and she has my contact details for if she ever wants to contact me in the future.
it is hard being without family, but good friends are just as valuable, and you get to chose those.
be kind to yourself, if you wish to attend your mums funeral or whatever then do so, if you feel you don't want to go that is ok too, it is all about you and your feelings at this time not how others feel or think you should do. you are bound to grieve, not only the loss of your mum and any hopes of an apology or reconcilliation, but the emptiness left by the hatred for her too because hating the person who hurt you when they are alive is a completely different hatred than that when they are no longer able to ever answer to their actions.
take care, be kind to yourself and accept that your emotions have a long road to travel before you will feel some peace over all that is/has happened and you can get on with the next chapter of your life x