Parents are actually required to send the kids to public school. There four options for parents not wanting to send their children into an unhealthy environment.
1. Home-schooling
2. Private School
3. Boarding School
4. Tutor
All of these will end up costing a significant amount of money though... I was home-schooled all through elementary and now as a senior in high-school, have found myself to be extremely thankful for those extra years at home with my mother teaching me the basics. We also used the same textbooks the public schools use and we had satellite videos from an educational facility that were created directly for the at home student. It was great!

You can home school, alternative school, magnet or private schools.

No you don't have to send them to a public school in the United States. Our oldest 2 went to private school, until they started 6th and 4th grade. We felt at this time there were more opportunities available to them in a public school setting (that, and we couldn't afford tuition anymore) I was homeschooled, but that is not really an option I want for my children.

Parents don't have to send their children to public schools. They can send them to private schools or hire private tutors if their checkbook permits.

My parents refused to send my brother and I to public school because the ones where we lived had poor pupil performance so we went to private school.

No they should not be forced to send their children to government/union schools. These places are mostly used for brainwashing.