What is the Sharia ruling regarding the oath: "By divorce, I will not enter your house again," if the husband then entered his wife's family's house the very next day? And is expiation required by feeding ten needy people or fasting for three days?

The husband is bound by the divorce he swore by, and the wife is divorced due to his breaking of the oath, according to the majority of scholars, and this is the most preponderant opinion. The husband may take back his wife before the expiration of her 'iddah if this was the first or second divorce. He must be careful about swearing by divorce and toying with it.