Who file the support papers? Was it the mother, or the grandmother? I have read through a few of the responses (not all) and I must say, that some well meaning ladies may have given you misinformation. I worked in child support enforcement for 10 years for a contract attorney representing custodial parents for the State of FL. We dealt specifically with inTER-state child support (meaning one party resides in one state and the other party resides in a different state). Every state has different laws regarding how long support is required. It is true that MOST states require it through age 18, or up until 19 so long as the child is a student in high school not yet graduated. However, there are a few "oddball" states (and I believe that NY is one of them) that support continues until age 21. There can also be additional requirements regarding health insurance, medical reimbursement and college expenses depending on the state in which the order is entered and the specifics of each particular case.
Please consult with an attorney familiar with the laws of your state and the laws of the state which ISSUED the support order (they may not be the same, if the parties were divorced in NJ but then moved, for example). Without a copy of the support order(s) in that particular case, none of us can tell you exactly what is required. However, that said, the mother has no standing to file for support if she is not the custodian of the child. The grandmother, however, can.