Have you applied for your daughter to get the benefit yet ? I think it was a seperate step from the regular ssdi benefits application.

If your daughter lives with your ex, the check goes to that household and your ex can "blow" it the way she would blow any CS.

Are you already paying CS ? Where your dd is so close to 18, if you don't owe your ex arrears on CS, maybe you could call social security and ask if they would hold your application for dd's benefits for a few months til she turns 18 and she could keep the backpay for herself.