Does divorce occur with the statement, "If you leave the door, you are divorced," when the wife does not leave at that time, and then her husband gives her permission to leave later? And is the couple's sexual intercourse after that considered a return of the wife without intention or utterance? And is expiation required for that after years have passed and children have been born?

As long as you intended to prevent your wife from leaving only at the time of the quarrel, and she did not leave then, you have fulfilled your oath. Therefore, your wife is not divorced if she leaves again, because your oath does not necessitate repetition. Ibn Qudamah said: "The conditional particles (إن, من, إذا, متى, أي) do not necessitate repetition of divorce, except for (كلما)." Accordingly, your divorce has not taken effect, and no expiation for an oath is required of you.