How can one deal with a family that opposes their daughter marrying a divorced man who is separated from his wife, knowing that the marriage will be legitimate and legal, and is it permissible to conceal from the family the fact that he is not [yet] divorced?

The fact that a man is married to another woman does not prevent marrying him Islamically. Rather, Islamic law commands accepting a compatible spouse. If the man is pleasing in his religiosity and character, then your family has no right to prevent you from marrying him. You are not obliged Islamically to inform them that he is married. It is permissible for you to use dissimulation (tawriyah) by informing them that he does not have a wife, meaning his separation from her. If your family discovers the matter and you fear their harm, then seek help from the wise people among your family or others whose words would be accepted by them.