Did the divorce occur in the mentioned cases, which are: uttering a divorce oath in a state of extreme anger, saying "consider her divorced" to her brother in a similar state of anger, and sending a text message of divorce by saying "You are divorced and I will not tolerate you again, enough"?

If you uttered a divorce to your wife with an explicit pronouncement, or with an implicit one intending divorce, then the divorce has occurred. Similarly, a conditional divorce takes effect upon breaking the oath. Your statement to her brother, "Consider her divorced," is an implicit divorce pronouncement by which divorce takes effect with the intention, as does divorce via a mobile message written down, which takes effect with the intention. The ill-temperament and insubordination of the wife permit the husband to deal with her according to Islamic law. If her condition improves, then that is good and blessed; otherwise, divorce may be better than retention, because the continuation of the marriage may become pure corruption and harm. The interference of family members when it is not in the interest of the spouses further complicates problems. The wife must reside where her husband resides unless there is a legitimate impediment preventing her. Anger does not prevent the occurrence of divorce unless the person reaches a state where he does not comprehend what he is saying. Slapping cheeks and tearing garments during a calamity is not from the character of the people of Islam.