Is the wife divorced merely by her husband returning to his divorced wife, given that he swore an oath of divorce upon her in the event of his return to his former wife?

If the husband has divorced his new wife with three pronouncements of divorce, she has become irrevocably separated from him, and she is not lawful for him until she marries another husband. However, if he divorced her with less than three pronouncements, he has the right to take her back before the completion of her iddah (waiting period). Suspending divorce and prohibition on her returning to him in the future does not necessitate a breach of an oath (hanath) unless she actually returns to his marital bond.

As for the detailed ruling: 1. Conditional Divorce: It takes effect upon the fulfillment of the condition according to the majority of scholars, and this is the most preponderant opinion. Sheikh al-Islam Ibn Taymiyyah stated that an expiation for an oath (kaffarat yamin) is required if he did not intend a divorce. 2. Prohibition (Tahrim): The ruling depends on the husband's intention: If he intended divorce and intended it to confirm the first one: one pronouncement of divorce is binding upon him. If he intended to initiate it: two pronouncements of divorce are binding upon him. If he intended zihar (analogizing his wife to an unmarriageable kin): it becomes zihar. If he intended an oath by Allah Almighty or did not intend anything: an expiation for an oath is binding upon him.

It is forbidden for a wife to ask her husband to divorce his other wife.