This is a complicated matter since there are two states involved. The simple answer is yes you can file for custody of a child in another state if you live in New York; however, whether you can do it before the child is born is a different issue.
You should contact the Clerk of the Florida Court in which you made the request. Child support obligation in Florida terminates when the child is 18 years old. Child support terminates in New York when the child is 21 under most circumstances.
You have jurisdictional issues which need to be reviewed with a lawyer; however, by the facts as you presented them, you have legal recourse if you can prove that the children are not in school. Jane.Bevans.esq@gmail.com