Does divorce take place if the husband says to his wife: "If you want separation, then divorce me, for I will never divorce you," and then the wife replies with "A day will come when I divorce you" or "I divorce you" after a period of quarreling, knowing that intercourse and normal life occurred during this period?

Divorce is a right of the husband, and he may delegate this right to his wife. However, the statement mentioned by the husband is not considered a delegation. If the husband intended that he would not divorce unless the divorce came from the wife, then what she issues has no effect. Even if it were considered a delegation, the wife's inquisitive statement "Shall I divorce you?" or "A day will come when I divorce you" is not a divorce. The spouses must strive for understanding, strengthen their relationship, and not allow room for Satan to sow discord between them, especially with the presence of children.