What is the Shar'i ruling regarding a wife who leaves her husband's house without his knowledge, when her husband has sworn an oath of divorce upon her if she does so?

Most scholars hold that conditional divorce takes effect when the condition is met, whether the intent was to pronounce divorce or to threaten. This is the prevailing fatwa. However, Sheikh al-Islam Ibn Taymiyyah is of the view that if the husband did not intend to effect a divorce, but rather intended to threaten or prevent, then no divorce occurs, and he must offer expiation for a broken oath (kaffarat yameen). Therefore, if you conditioned your wife's divorce on her leaving without permission, the prevailing fatwa with us is that she is divorced by her departure, and if her waiting period (iddah) has ended, she is irrevocably separated from you and cannot return except with a new marriage contract. As for the view of Sheikh al-Islam, her divorce did not occur if you intended a threat, and you must offer expiation for a broken oath. It should be noted that threatening with divorce is an unsound approach, and the prescribed method is to use legitimate means of reconciliation.