There are many proponents of a so-called Parental Rights Amendment, an actual amendment to the actual Constitution. HSLDA is one of the organizations that support it. (Beware the "it's almost too late, look what happened with gay marriage" alarmist argument at the beginning of the article! Honestly.)
The idea behind this amendment is that until and unless there is specific language in the Constitution defining and declaring that parents have a right to raise their children as they see fit, then there can be no real protection against government interference in legitimate parental issues.
I think this idea, while well-intentioned, is backwards. Because rights are not issued to us from the Constitution--they are objective and derived from reality and the Constitution exists to protect those rights. In other words, just because a right isn't specifically named in the Constitution doesn't mean it isn't a right and you aren't entitled to protection from violations. (If you can work your way through all those negatives, that sentence might make sense!)
Man holds these rights, not from the Collective nor for the Collective, but against the Collective—as a barrier which the Collective cannot cross; . . . these rights are man’s protection against all other men.
--Ayn Rand, “Textbook of Americanism,” The Ayn Rand Column, 83.
The source of man’s rights is not divine law or congressional law, but the law of identity.
--Ayn Rand, Galt’s Speech, For the New Intellectual, 182.
(Above quotations via the online Ayn Rand Lexicon)
And also, here's the 9th Amendment, already in the Constitution:
The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
We parents, we're already covered, by virtue of the fact that we are American citizens. (You might be thinking about the 14th and 19th Amendments, which were not special-interest-group kinds of Amendments. They corrected fundamental errors that existed in the original writing of the Constitution.)
An recent article by Larry and Susan Kaseman of Home Education Magazine spells out many of the ways in which a Parental Rights Amendment would create more problems than it would solve. It's an interesting read. I especially liked the "What We Can Do" section because it illustrates the many ways in which we can be proactive in protecting our rights (which exist outside of an official Amendment). It's something we should all do in every area of our lives, every time our rights are infringed upon. Just a few examples from that section (emphasis mine):
What We Can Do• We can be aware of the challenges to parental rights, keep up to date, and watch for developments that require response. We can inform others through informal conversations, support group meetings, letters to the editor, etc.
• We can continue to homeschool our children and exercise our rights in other ways, including taking responsibility for decisions involving our children's growth and development, health care, and moral and spiritual development. By actions such as these, we increase our confidence and ability to take responsibility for our families and our lives. We set an example for other parents and help them understand what options they have and how capable they are. We also set an example for our children.
• We can object when our parental rights are challenged and insist that they be respected, whether it be officials implying that we are legally required to bring our children in for preschool screening, school officials demanding to review and approve our homeschooling curriculum in states that do not require this, medical personal asking personal questions not required by law during a routine check up or an emergency room visit, or other such situations. We can avoid setting precedents that will cause problems for other parents and possibly for us in the future by not voluntarily complying with requests or demands from officials that exceed their authority under the law. When an official tells us that we must do something, we can ask for a copy of the statute that requires such action.
Lots of people are confused as to the proper role of government. We don't work for them--they work for us. When they step out of line, it's up to us to help them step back over. That doesn't usually entail passing more laws or Constitutional Amendments. (The occasional thwack on the forehead might help, though.)