Does divorce take place if a man says to his wife, "If you send me messages of insult and slander, then you are divorced," and then she sends him a message of insult and slander, knowing that he intended to threaten her and that this was the third divorce?

Your instruction to your daughter to inform her mother about the suspended divorce is equivalent to informing your wife directly. The majority of scholars hold the view that a suspended divorce takes effect upon the fulfillment of the condition, and this is the preponderant opinion. If your wife did indeed send you messages of insults and curses, as you mentioned, then according to the majority of scholars, the divorce has occurred. If this was the third divorce, then your wife has become irrevocably separated from you (bainunah kubra), and she is not lawful for you until she marries another man a valid marriage and he then divorces her after consummating the marriage. Sheikh Al-Islam Ibn Taymiyyah and those who agree with him are of the opinion that you are required to offer an expiation for breaking an oath (kaffarat yameen) if you did not intend divorce but rather intended a threat; however, the preponderant view is that of the majority of scholars. It is not permissible for your wife to harm you with insults or curses, and it is more befitting for her to treat you well.