Child support payments are made to the parent or caregiver or the child - not to the child itself. The money that is owed is money that belongs to your nana that was to be used to raise you, feed you, cloth you, etc.
You have no legal rights to the money and therefore can not sue your dad for it. Only your nana could file a suit and even then - the money would go to her and not you.
Your nana has to step up if she wants any support, my gf's dad is the same way but her mom hasn't done a thing about it :/
In the eye of the court your nana has to be the one to sue
it should be your nana suing... not you.