Does the divorce take effect by saying "you are divorced" in the context of a violent quarrel and in response to the wife's transgressions, then repeating the same statement later while talking to oneself, with the intention of not enacting the divorce the first time, and with the questioner's desire to preserve his children?

The spouses must treat each other kindly. It is forbidden for the wife to seek divorce without a legitimate Shar'i excuse, and it is forbidden for the husband to beat his wife severely. The husband's statement "You are divorced" is considered an explicit divorce and takes effect without requiring intention. What one says to oneself or utters in the bathroom does not constitute a divorce. The husband may take his wife back before her 'iddah (definition) is complete, provided this divorce does not complete the three divorces, and the wife's consent or knowledge is not required for the return. If the 'iddah expires without a return, the husband can remarry her with her consent and her guardian's permission.