Would the husband have fulfilled his oath of divorce - which he swore due to his wife's repeated actions during a quarrel - when he lightly struck her after she repeated those actions, knowing that he told her he was only threatening her?

The majority of jurists hold that swearing an oath by divorce — whether intended as an actual divorce, a threat, a prohibition, an encouragement, or an affirmation — results in the occurrence of divorce upon breaking the oath. This is the prevailing fatwa. This differs from the view of Sheikh al-Islam Ibn Taymiyyah, who considers its ruling to be like swearing an oath by Allah, such that if one breaks the oath, an expiation for an oath becomes incumbent, and divorce does not occur. Accordingly, if the wife contravenes what the husband swore an oath upon, and he does not carry out what he threatened, divorce occurs. The reference for what he threatened is his intention and aim; so if he intended a painful beating, he is not absolved unless he carries it out. The matter should be presented to the Sharia court or to trustworthy scholars to ascertain the husband's intention.