I have an update to this for those of you who are interested :)
I have to say, at first I was very optimistic and I thought that my grandmother dying might have created new possibilities for communication between my mother and me. When I sent her that letter, she replied that she "understood more than I was aware of" and she said that she deeply regretted the way she treated me, viewing her own "malice" as the same frenzy an animal experiences when in extreme pain.
So far so good. I went to visit her and my uncle the day afterwards. It was more difficult than I expected - I suffered from severe anxiety in the train - more than usual - panicked, self harmed and had a very hard time not seeming completely insane to all the other travelers. When I got out of the train, I fled to the isolated part of the platform and sat there just hitting myself and my bike and I had no idea what to do. In my heart I wanted to go home and not deal with her.
I called several people, of whom nobody picked up, and after an hour my uncle called and they finally offered to come pick me up. My mother had made a rather depressing dinner consisting of canned soup and buns - I did not dislike it, but it made me sad, because our gathering seemed rather uncomfortable. We chatted about completely dull things - superficial talk - until I couldn´t take it anymore - then I said I was going out for a walk. I called a friend of mine, who helped me.
I went back in, and it was better now, they seemed to have relaxed a little bit and I was feeling less tense on account of talking to my friend. We finally conversed about something meaningful (my grandparents and church). Then my mother left and my uncle offered to take me back to the train station. I offered to come visit him more often, to which he said yes and it seemed very genuine. During the dinner I had also asked my mother if she could possibly spare some money.
I did not request it forcibly, I just said "if" she could spare any, I could use it. I had invested quite a lot of money in good clothes and shoes for the funeral, considering I only had crappy clothes that I would not have dared to wear. She said that she could help me with that. A week later, I got an email from her in which she stated that she could not give me any money, because, I would never share anything about my life with her and I never did anything for her, so I did not quite deserve anything in return.
This angered me quite a lot. During the funeral I was there to support her, I sent her several messages saying that I hoped she was okay (prior to the funeral). I gave her a present which was sort of symbolic because I had it specially made. I wrote her that lengthy letter explaining my emotions. And then I went through the trouble of dealing with that train ride, hurting myself, and seeming completely insane to the other passengers. In short I think I have done what I could for her.
I wrote back that it seems that I can never be what she wants me to be. I think she misunderstood my entire letter. If she thinks I´m an evil child for not conforming to her expectations of me, she obviously does not understand why I don´t write her more often, and she obviously does not forgive me for not doing so.
In short: we´re back were we started. Maybe abusers never change after all.
I don´t know. I hope other people have better luck.