Does a divorce take effect if I said: "If my wife leaves the house door with her brother, she is divorced," then I let her brother leave alone, and I escorted the wife out the door and delivered her to her brother?

The oath is based on the intention of the swearer. So, if you intended to make your wife's divorce contingent upon her leaving the house through the door accompanied by her brother, then the divorce will not occur if you yourself take her out through the door of the house and then take her to her brother in another place. However, if you intended to make the divorce contingent upon her merely leaving and accompanying her brother, then the divorce will occur as soon as she leaves with him. The breach of the oath occurs when what you intended in your contingency happens. If you had no specific intention, then the apparent meaning of the wording is what matters. The apparent meaning of your statement: "If my wife leaves the house through the door with her brother, then she is divorced," implies making the divorce contingent upon her accompanying her brother when leaving through the door of the house. Based on this, she will not be divorced by the method you used to take her out. The occurrence of divorce – in the situation where it occurs – is the view of the majority of scholars. It is also said that an expiation for an oath is due if you did not intend a divorce.