You might not like it, but it's been the law of the land for a long time (at least 50 years, probably more like 100). If you choose to have children in the USA, state law determines (for a whole host of reasons) that you have a set of obligation to those children. Among your obligations as a parent is to see to it that your child gets a state-certified education.
If you don't like it, you have three reasonable options:
1. Work through the system to change the law.
2. Don't have children.
3. Move out of the USA.
I hope that the police coming to take the O'Dell kids into custody was not the first contact that she's had with the child protection authorities. I hope that it is a just situation and this woman has had lots of opportunities to provide for her kids and refused them unreasonably just like she seems to have unreasonably refused to be finger-printed.
Around 1852.