How can a girl tell her family of her desire to marry a married man, and is it better for her to approach them or for the man to speak to them?

A man should propose to you, and then you can express your approval to your family. Your family is not permitted to prevent you from marrying a compatible man whom you desire. If they do prevent you, guardianship transfers to the next closest relative, and then to the religious judge (hakim shar'i). If the family refuses, we advise you to refrain from marriage to avoid conflict, especially if the refusal comes from the parents; unless this would lead to falling into sin or severe harm, in which case you can refer the matter to the judiciary.