My kids are moving to Georgia with their father who is not on the birth certificate nor the custodial parent, this is with my permission but what legal documents are required for him to enroll them in school and to authorize medical care, etc?

Call the school or school district and ask those questions of the enrollment office. They will tell you about paperwork , immunization records, and transferring records from the old school.

In Georgia it is not suppose to happen, legally he is a stranger to them. He is not legally the father, since he is not on birth certificate or proven father though a court order.

It would be like me trying to enroll them. They will need you to come down and enroll them in school. Or he will have to be given temp guardianship.