Each state Constitution is different. For instance, there's nothing in the Texas Constitution that deprives it of requiring vaccinations for state funded facilities. As Madison said, the powers of the Federal Government are few and defined. Those which are to remain in the State governments are numerous and indefinite.
I also don't see anything in the Constitution requiring compulsory education in a public school, which is not something I'm advocating, and is irrelevant to the topic.
Keep your kids home for all I care.