Is it permissible for a woman to continue her marriage to a man addicted to drinking alcohol and staying out late, given the presence of children, her suffering from estrangement, and the husband's disclosure of their secrets?

It is permissible for her to remain with her husband if she feels safe for herself and her children, and if his disobedience does not reach the level of disbelief (kufr). She must assess her own best interest, consult her family, and then seek Allah's guidance (istikharah) in her matter. She should accept Allah's decree, be patient, and seek reward from Him.