As to point 1...
Homeschooling doesn't exist to support parental rights to freedom of expression or freedom of religion, although many groups have interpreted homeschooling laws from this angle. These homeschoolers and taken increasingly anti-educational positions to further entrench a damaging, extreme form of libertarianism that only really forwards the agenda of the parent, at the expense of the child.
For fundamentalist homeschoolers, it's not so much a view of "I'm for freedom of education" so much as "I'm against THAT value system and reject any association with it." The children become an objectified extension of the parent's identity, not individuals with their own inalienable rights who ought to be recipients of an individually-appropriate education.
Yes, exactly. Excellent way of stating the problem.