What is the ruling regarding a man who warned his son not to smoke in the house—knowing that the house is rented—otherwise his mother would be divorced, and then the son smoked in another house different from the first?

If you made the divorce conditional on your son smoking at home, then if this was intended as a promise, divorce does not occur unless you fulfill the promise. However, if it was a condition based on his smoking at home, it is a conditional divorce, and according to the majority of scholars, it takes effect if you did not intend a specific house. Sheikh al-Islam Ibn Taymiyyah held that an expiation for a broken oath (kaffarat yameen) is required if you did not intend divorce but rather a threat. And if there was a reason to prevent him from smoking in the first house and that reason ceased to exist in the second house, then divorce does not occur.