You did the best thing. Keep it simple....send the bill and let him know when his payment is due. You can't make him a good Dad. If he refuses to help, then he refuses. But don't let him make the money based on conditions. Don't give him that kind of power over you OR your daughter.
I would move forward as if there will be no money. Look into all other options. That way if he does pay, it's a bonus.