What is the ruling regarding someone who swore an oath of divorce upon his wife, in a state of extreme anger, concerning a matter (which was leaving the shop after an argument with a partner), but he did not leave? What are the consequences of that?

This oath is considered a conditional divorce, and according to the majority of scholars, divorce occurs upon the fulfillment of the condition. However, Shaykh al-Islam Ibn Taymiyyah holds that divorce does not occur if the intention was merely to prevent or encourage something.

Since the oath was in the form of a broken oath (if I do not enter the house, then you are divorced), it is not permissible for you to approach your wife until you dissolve the partnership, unless you conditioned the oath on a specific time that has not yet expired.

The Malikis are of the opinion that one is prohibited from approaching his wife until he fulfills the oath, and a deadline for an ila' (oath of abstinence) is set for him. The Hanafis, on the other hand, held that the oath is not broken until there is despair of fulfilling it, and thus it is permissible to enjoy one's wife until that time. It is recommended to consult one of the Islamic centers.