What should I do regarding a man proposing to me who is already married, given my family's disapproval and the fact that he has a daughter which prevents him from divorcing, and is there any role for me to play?

If the man you wish to marry is of good religious observance and character, strive to convince your parents to agree to him, and seek help from Allah, then from those who can influence them. If they agree, then praise be to Allah. But if they refuse, the default is that you must obey them, unless you fear severe harm to yourself due to delayed marriage, or their refusal is unjustified. In such a case, you are not obliged to obey them, and you may resort to the Sharia judge to marry you, while still being keen on their رضا and dutifulness towards them.