What is the ruling on a girl traveling to another city to seek knowledge with her mother's consent but her father's refusal, given that he relies heavily on her for household matters, and she fears her father's displeasure if he agrees, and she desires not to stir up conflict between her parents?

It is advisable to combine learning the Quran with staying with the father in his home, if possible. If that is not possible, then it is better to stay with the father and strive in honoring him, for it is one of the greatest acts of closeness to Allah and most beloved deeds to Him, and among the reasons for Allah's help and success in beneficial knowledge and righteous deeds, and entering Paradise; because the Messenger of Allah, peace and blessings be upon him, said: "The father is the middle gate of Paradise, so if you wish, abandon this gate or preserve it."