Is a man considered a "dayyuth" if he marries a woman who does not fully adhere to the شرعي (Shar'i) hijab, knowing this beforehand, and is unable to monitor her or ensure her adherence in his absence, even though he is committed himself and has tried to advise her?

A man is responsible for his wife by virtue of his guardianship (Qawamah). He is to prevent her from corruption and oblige her to fulfill her duties. If the husband fulfills his duty and then the wife commits a wrongdoing in his absence, he bears no sin for it, and the sin is hers alone; for the original principle in Islamic law is that no one bears the sin of another.