Does the divorce occur by the words: "Divorce upon me, if he leaves the house, you will follow him to your family's house, and he will not leave except with my permission," if the son went out to the grandmother's apartment, then was brought back and taken out to the street, knowing that the statement was made with an unconfirmed intention and in a state of extreme anger, and the wife is pure?

The first phrase could mean divorce or something else, but your statement: "He will not go out except with my permission" is an explicit oath of divorce concerning your son not leaving without your permission. Since your son did leave without your permission, a divorce has occurred according to us, whether you intended to enact it or merely threaten. Your intercourse with your wife during this period of purity does not prevent the divorce from occurring. Some scholars hold that your divorce has not occurred as long as you did not intend to enact it, and you are liable for an expiation for breaking an oath. The prescribed oath is to swear by Allah the Almighty, while swearing by divorce is among the oaths of the dissolute.