You most likely will not have to pay additional child support for your granddaughter. You might need a good attorney to argue this fact however.
It is unlikely you would be obligated to pay additional child support for your grandchild. The person that should be paying child support for the grandchild is the grandchild's father. You can also go to court for a modification of support, if you feel as though you should not be supporting your daughter until she is 23, if she is not in school.