Prohibiting child abuse is within the police power of the government. perhaps this case will help you understand the law in this area:
Santosky v. Kramer
Today we hold that the Due Process Clause of the Fourteenth Amendment demands more than the "fair preponderance of the evidence". Before a State may sever completely and irrevocably the rights of parents in [p748] their natural child, due process requires that the State support its allegations by at least clear and convincing evidence.
if convinced that "positive, nurturing parent-child relationships no longer exist," § 384-b.1.(b), the State may initiate "permanent neglect" proceedings to free the child for adoption.
The State must further prove that the child's natural parents failed substantially and continuously or repeatedly to maintain contact with or plan for the future of the child although physically and financially able to do so.
State intervention in domestic relations has always been an unhappy but necessary feature of life in our organized society. For all of our experience in this area, we have found no fully satisfactory solutions to the painful problem of child abuse and neglect. We have found, however, that leaving the States free to experiment with various remedies has produced novel approaches and promising progress.
See However:
Ingraham v. Wright
Today the Court holds that corporal punishment in public schools, no matter how severe, can never be the subject of the protections afforded by the Eighth Amendment. It also holds [p684] that students in the public school systems are not constitutionally entitled to a hearing of any sort before beatings can be inflicted on them.
I doubt I have to explain my point in citing the Ingraham case.