>> First thing she said was that I have to become worthy of my father.

You don't need to be worthy of anyone but yourself. That is manipulation that parents/grandparents do on their children and it's horribly destructive as it will only riddle you with guilt. F** living up to your father, do the things that vibe with you.

Your sister will (somehow) need to come to terms that $$ is needed in life. If money is scarce then stop paying for her lessons and tell her to get a part time job as she must come to understand asap that things cost $$ in real life.