Does divorce take effect if the husband said to his wife: "Divorce be upon me that no one from the children will enter the house," then one of the sons entered the house without his knowledge, knowing that the intention was to prevent the children from entering and not to effect a divorce?

What your brother issued was a conditional divorce of his wife upon one of his children entering the house, and indeed one of them has entered. There are four schools of thought regarding this issue: The Shafi'i school holds that the divorce does not occur if the entry was by忘れ (forgetfulness) and he had knowledge of the oath, or if he was ignorant of it. The Maliki, Hanafi, and Hanbali schools, which is our preferred view, hold that the divorce occurs upon the fulfillment of the condition without any further detail. The school of thought of Sheikh al-Islam Ibn Taymiyyah holds that only an expiation for an oath is required if there was no intention of divorce. And the school of thought of Ibn Hazm holds that the divorce does not occur in any case. Our preferred view is that of the majority. Therefore, your brother may take back his wife before the completion of her iddah (waiting period) if this divorce does not complete three divorces. Her iddah ends with her purification from the third menstrual cycle after the divorce, or after the passage of three months if she does not menstruate, or upon delivering her child if she is pregnant.