What is the ruling regarding the divorce pronouncement I uttered to my wife in a moment of anger, knowing that she had previously written a statement expressing her desire for divorce, but my intention was not actually to divorce her, and the problem escalated due to my brother's interference?

If you uttered the divorce while being aware of what you were saying, then your divorce is effective. You can take back your wife before the expiration of her waiting period ('iddah) if this was not the third divorce. Her waiting period ('iddah) expires with her becoming pure from the third menstruation after the divorce, or after the passage of three months if she does not menstruate, or by giving birth if she is pregnant. If the waiting period ('iddah) has expired, she is not lawful for you except with a new contract that fulfills the conditions for a valid marriage. However, if this was the third divorce, then she is unlawful for you and does not become lawful again until she marries another husband in a valid marriage and he then divorces her after consummating the marriage.