It has been interpreted by that country's laws in certain ways, absolutely. It is not what it's made out to be though. Most of the rhetoric stems from ParentalRights.org and in particular this: http://www.parentalrights.org/...{550447B1-E2C1-4B55-87F1-610A9E601E45}
If you read through their citations though you'll notice they start off by mentioning the Vienna Convention on the Law of Treaties - the US has not ratified that treaty. Then they go on to quote the constitution...
This Constitution, and the Laws of the United States which shall be made in pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding
This is particularly interesting because the US has already ratified "International Covenant on Civil and Political Rights". In doing so they declared that Articles 1-27 were not self-executing. This meant that congress had no obligation to implement the provisions in law. However, they did not make the exception of the remaining articles meaning they are self-executing (Medellin v. Texas).
Article 50: The provisions of the present Covenant shall extend to all parts of federal States without any limitations or exceptions.
This means that the Supreme Court as well as State legislatures are obliged to adhere to all the articles. This is further backed up by their statement of understanding:
(5) That the United States understands that this Covenant shall be implemented by the Federal Government to the extent that it exercises legislative and judicial jurisdiction over the matters covered therein, and otherwise by the state and local governments; to the extent that state and local governments exercise jurisdiction over such matters, the Federal Government shall take measures appropriate to the Federal system to the end that the competent authorities of the state or local governments may take appropriate measures for the fulfillment of the Covenant.
So what does that mean? Likely a court challenge to get the supreme court to apply something like the "Baker" principle (there is precedent for it):
The Baker decision thus establishes the principle that, in the process of statutory interpretation and in matters of judicial review, it is entirely appropriate to rely on provisions of international conventions which have not been incorporated into legislation but with which the State is presumed to have a will to be in compliance.
Once that is done articles 1-27 come into effect in practice:
Article 17
1. No one shall be subjected to arbitrary or unlawful interference with his privacy, family, home or correspondence, nor to unlawful attacks on his honour and reputation.
2. Everyone has the right to the protection of the law against such interference or attacks.
Article 18
1. Everyone shall have the right to freedom of thought, conscience and religion. This right shall include freedom to have or to adopt a religion or belief of his choice, and freedom, either individually or in community with others and in public or private, to manifest his religion or belief in worship, observance, practice and teaching.
2. No one shall be subject to coercion which would impair his freedom to have or to adopt a religion or belief of his choice.
3. Freedom to manifest one's religion or beliefs may be subject only to such limitations as are prescribed by law and are necessary to protect public safety, order, health, or morals or the fundamental rights and freedoms of others. 4. The States Parties to the present Covenant undertake to have respect for the liberty of parents and, when applicable, legal guardians to ensure the religious and moral education of their children in conformity with their own convictions.
There's the protection against the craziness that is spouted by ParentalRights.org - and even if that should not exist, the law is quite clear that the US constitution trumps any international agreement so anything that is currently protected under the constitution will remain so after ratification. So many of these organizations don't understand that international law is not like domestic law - it's viewed as a whole, not part by part.
Many point to things like the German SWAT team that stormed a family's house because they were being home schooled and blaming that on the CRC... in reality it was actually a German domestic law that made home schooling illegal.
I will admit that there are some laws which may change the parental rights in the US, but only so far as they are constitutional. I suspect corporal punishment would be one of them. That said, Canada ratified the treaty a couple decades ago and still has a corporal punishment law on the books for parents. They also allow it in the military.