I think the OP's problem is that if the daughter is moving out after graduation, but before she is 18 - he would like the payments that he is paying to be FOR the daughter. But, he cannot dictate the terms. If she isn't living with mom, is mom just pocketing the money for a year? Or does he even know if mom wouldn't be forwarding the money to the daughter?
If he wants to stop payments after she graduates and she moves out, daughter needs to file for emancipation. Otherwise, LEGALLY, he has to continue paying the support until 18.