Just out of curiosity, what did you expect the response to your letter to be?

Your grandparents have been who they are for a long time - they won't substantially change no matter how well-written or emotionally resonant your letter was. In my experience people just aren't wired that way.

If your family is toxic to you, maintain distance. Avoid dependence, don't let anyone do you favors (as they can be used as leverage), and seek out healthy relationships instead of trying to fix toxic people. Even if it is harder you may find that moving out and being self-sufficient is more personally rewarding than living dependent in your current lifestyle. Many people support themselves with loans and work through college - it is difficult but not impossible.

Honestly you come off as quite judgemental yourself. Remember that you are criticizing your aunt for doing basically what you are doing now (relying on her parents to maintain her lifestyle). If you want to be as judgemental towards your aunt as you come off here for accepting money from her parents, you are a hypocrite unless you are independent yourself. The rest of her behavior seems to have nothing at all to do with you - I don't know why you are taking it personally how she relates to other members of your family. You also live at a standard you can't afford. You also are not attending family functions. You and the rest of your family spend time insulting her behind her back with your other family members, and then act shocked that she is distant and removed?

If you write letters, write them for yourself, in order to better express and understand yourself. You can't change people with letters. You can't control their reactions to them. You can only control and affect yourself - and you probably shouldn't judge people without being absolutely perfect yourself.