Does a divorce occur if the wife goes to her husband's family home with his father's permission, after the husband conditioned the divorce on her leaving without his permission, and the husband had ceased communicating with her, and the wife understood that the husband's family home was an exception to the oath?

If the husband gave you absolute permission to go to his family's house, then divorce did not occur by your departure after three days. However, if his intention was to permit it only for that specific day, and you went, thinking he had given absolute permission, then the preponderant opinion is also that no breach of the oath has occurred. This is because you acted based on an interpretation and a belief that no breach would occur, and this is more deserving of exemption from breach than the case of someone who acts out of ignorance or forgetfulness. This is supported by the statements of Ibn al-Qayyim and the fatwas of the Permanent Committee, who cite the noble verse: {And there is no blame upon you for that in which you have erred, but [there is blame for] what your hearts intended} and the hadith: "Indeed, Allah has overlooked for my Ummah their mistakes, their forgetfulness, and what they are compelled to do." Therefore, the absence of an intention to violate prevents the breach of the oath.