Is the wife considered divorced if the husband says, "If you go out, then you are divorced," and she goes out, knowing that this is the first divorce? And is the husband bound by anything if he takes her back before the 'iddah (waiting period) ends? And does she have the right to stipulate anything upon her return?

The Messenger of Allah, peace and blessings be upon him, advised against anger, because anger causes a person to lose control of himself and makes him act in a way that leads to regret.

If your intention in speaking to your wife was merely to threaten divorce, not to make it contingent upon her leaving, then scholars have differed on this matter. The majority of them hold that divorce occurs when she leaves. However, some have opined that she is not divorced from you because this falls under the category of threatening divorce, and you are required to offer expiation for breaking an oath (kaffarat yamin).

However, if you intended to make her divorce contingent upon her leaving, then she is divorced with a single divorce immediately upon her departure.

You have the right to take her back before the expiration of her 'iddah (waiting period) without a new contract, or mahr (dowry), or wali (guardian), or witnesses (though witnessing is recommended), and without her consent. The return can be by explicit verbal declaration, such as: "I have taken you back," or by implicit words, such as: "You are my wife," with the intention of taking her back, or by action, such as sexual intercourse and its preliminaries.