Has divorce taken place with the words "you are divorced" uttered twice in a state of extreme anger and without the intention of divorce? Is living with the wife in this situation considered unlawful, taking into account the birth of two daughters? What is the way out of this situation?

Your statement to your wife: "If you do not go to your family, I will divorce you" is a promise of divorce that does not effect it. As for your statement to her: "You are divorced," this is an explicit pronouncement that effects divorce, and repeating it in the same session effects another divorce. The wife's return (revocation of divorce) occurs by word or action. If you explicitly state your revocation, or if intercourse occurs while she is in her 'iddah (waiting period), the revocation is valid, the marital relationship continues, and the two daughters are attributed to you. Anger does not prevent the occurrence of divorce in all cases. One must be cautious of it and of making divorce a means to solve problems.