Is the wife considered divorced if he said to her "You are not my responsibility" twice, and she informed her family of their marital problems, knowing that she has been his wife for 25 years and they have no children?

A man's statement to his wife, "You are not under my responsibility (or protection)," is a form of allusive divorce (kinayah bi al-talaq (definition)), and divorce occurs if the man intends it. However, if he says, "Do not tell anyone, otherwise you are not under my responsibility," then if he intended divorce upon her informing someone, a revocable divorce occurs. But if he intended a threat and did not intend divorce, then it falls under the ruling of an oath, and an expiation for breaking an oath becomes obligatory upon her informing someone. It is encouraged to avoid divorce pronouncements and to resolve problems amicably, and to observe good companionship and good character between spouses.