Is the wife obligated to return to her husband's home after refusing to go there and his saying, "I want to get rid of her," and what is the ruling on this statement—does it constitute an irrevocable divorce?

The husband's statement: "I want to get rid of her" is not considered a divorce, even if he intended divorce, because it is a wish and not an enactment of divorce.

The wife must return to her husband's home, and it is not permissible for her to leave it without his permission; otherwise, she would be disobedient and rebellious (nashiz).

Sheikh Al-Islam Ibn Taymiyyah said: "So she (the wife) does not have the right to leave his house except with his permission, whether her father or mother, or anyone other than her parents, commands her [to do so], by agreement of the imams." Scholars substantiated this with the hadith: "If your women ask your permission to go to the mosque at night, permit them."