Does the first divorce occur if the husband says to his wife, "You are divorced if you leave," with the intention of frightening her, and then the wife leaves, forced by her father and not of her own free will?

The fatwa we adhere to is that your divorce has occurred. This is because the oath sworn by conditional divorce has been broken (al-hinth), and the coercion of the wife by her father to leave is not considered coercion that prevents the breaking of the oath unless the conditions for legally recognized coercion are met. These conditions are: that the coercer must have authority or dominance, that the coerced person must strongly believe that the threat will be carried out if they do not comply with the coercer, that they are unable to avert it, and that the harm inflicted upon them is significant. However, if the coercion is considered valid, then the divorce does not occur, and you are not required to offer expiation. Sheikh al-Islam Ibn Taymiyyah holds the view that if swearing by divorce is intended for emphasis, prevention, or encouragement, and not for the purpose of initiating a divorce, then divorce does not occur by it. Instead, the one who swore the oath is only required to offer an expiation for a broken oath (kaffarat yamin).