What is the ruling regarding a husband who prevents his wife from visiting her family because they previously exposed her to prostitution, even though the husband knows of her chastity and religiosity, and is she obligated to obey him?

If your family persists in their misguidance, your husband's stance in preventing you from visiting them is sound, and obedience to him is obligatory, because he is responsible for you. However, if they repent and their situation improves, then it is more appropriate that he does not prevent you from visiting them, especially your parents. You should make him understand that "the one who repents from sin is like one who has no sin," and that Allah forgives all sins.