http://www.flsenate.gov/Statutes/index.cfm?App_mode=Display_Statute&Search_String=&URL=Ch1003/Sec32.HTMTitle XLVIII K-20 EDUCATION CODE
Chapter 1003 PUBLIC K-12 EDUCATION
1003.32 Authority of teacher; responsibility for control of students; district school board and principal duties.-
(1) In accordance with this section and within the framework of the district school board's code of student conduct, teachers and other instructional personnel shall have the authority to undertake any of the following actions in managing student behavior and ensuring the safety of all students in their classes and school and their opportunity to learn in an orderly and disciplined classroom:
. . .
(k) Use corporal punishment according to school board policy and at least the following procedures, if a teacher feels that corporal punishment is necessary:
1. The use of corporal punishment shall be approved in principle by the principal before it is used, but approval is not necessary for each specific instance in which it is used. The principal shall prepare guidelines for administering such punishment which identify the types of punishable offenses, the conditions under which the punishment shall be administered, and the specific personnel on the school staff authorized to administer the punishment.
2. A teacher or principal may administer corporal punishment only in the presence of another adult who is informed beforehand, and in the student's presence, of the reason for the punishment.
3. A teacher or principal who has administered punishment shall, upon request, provide the student's parent with a written explanation of the reason for the punishment and the name of the other adult who was present.
Private schools generally have even more freedom, since attendance is by choice rather than mandate.
Even though corporal punishment is legally permitted in public schools, I would still support the parent in challenging the law with respect to public schools, since parents do not generally have an option to choose a different public school to send their child to. (If the child were older, I would also support the child who wanted to challenge either public school or parental disciplinary practices which involved corporal punishment.)
On the other hand, when you choose a private school for your child, you are entering into a voluntary contract with that school to educate your child in accordance with their practices. If you don't like their practices, the time to find out is before you enter into the contract - not to complain after the fact that you don't like the bargain you struck. (And yes, when I enrolled my daughter in preschool and childcare for after school when she was not old enough to stay by herself I did ask about disciplinary practices and would not have enrolled her anywhere that utilized corporal punishment.)