What should a daughter, over fifty years of age, do about her father's estrangement from her, her children, and her sister, after many years of abuse and injustice, and his rejection of all attempts at reconciliation? Is she sinful for not being able to approach him?

The default state for a father is compassion towards his children, and if his mistreatment is confirmed, it goes against that default. You have done well by seeking reconciliation with him, and you should make abundant supplication for his condition to change, and seek help from righteous people close to him. Do not despair, for Allah is capable of all things, and the hearts of His servants are in His hand. Strive to show him dutifulness to the best of your ability, for supplication and striving for his betterment are a type of dutifulness that includes bringing every good and repelling every harm according to one's capacity.