Is the questioner considered sinful for wishing for the death of her sick father, whom she cares for, in order to be relieved of the burden, while feeling guilty about this wish?

Taking care of one's father is a great and blessed act, which expands one's provision and lifespan, as narrated by Al-Bukhari and Muslim from the Prophet, peace and blessings be upon him: "Whoever wishes that his provision be expanded for him and his life lengthened, let him maintain ties of kinship." It is also one of the gates of Paradise, for he, peace and blessings be upon him, said: "The father is the middle gate of Paradise, so if you wish, squander that gate or preserve it."

The pleasure of Allah is linked to the pleasure of the father, as stated in the Hadith (definition) narrated by At-Tirmidhi: "The pleasure of the Lord is in the pleasure of the father, and the wrath of the Lord is in the wrath of the father." Therefore, one should not wish for the death of their father, for no soul will die until it completes its appointed term and receives its full provision. Provision is destined, and the lifespan is decreed.

One should believe in divine decree, and that no calamity befalls the earth or yourselves but is inscribed in a Book before We bring it into being. Relief can come through healing or marriage, not through death. Seek reward from Allah and frequently supplicate for yourself and your father for healing and well-being.