Does a divorce take place if the husband says to his wife: "If you go out, I will divorce you," and then she leaves the house and speaks with her brother to go to her family's home?

This wording used by your husband is a promise and a threat of divorce. Divorce does not occur merely by promising it. Sheikh al-Islam Ibn Taymiyyah said: "A promise of divorce does not constitute divorce, no matter how many times it is uttered, nor is it obligatory or even recommended to fulfill this promise."

Based on this, your divorce did not occur by your leaving the house, and your husband is not obliged to divorce you; rather, it is better for him not to divorce you. It is obligatory upon you to obey your husband and live with him amicably, and it is not permissible for you to leave his house without his permission unless there is a necessity.