What is the ruling regarding the wife going to her family's house after the husband swore an oath of divorce upon her, and declared her forbidden to him like his sister and mother if she goes, knowing that the husband intended for her to go at a later time?

If the wife goes to her father's house in this situation, divorce and ẓihār (a form of divorce by injurious assimilation) fall upon her. If the husband has not divorced her more than once, he can take her back during her ʿiddah (waiting period), but he should not have intercourse with her before expiating the ẓihār as mentioned in Surat Al-Mujadilah: freeing a slave; if he cannot find one, then fasting for two consecutive months; if he cannot do that, then feeding sixty poor people. The lawful oath is swearing by Allah Almighty. As for swearing by divorce or by declaring something ḥarām, these are oaths of the wicked.