The worst thing is that it exists. It's called the Convention on the Rights of the Child.
Guess what country is the only UN member state not to have ratified it. Oh, and it includes parents' rights too! It obliges states to allow parents to exercise their parental responsibilities and to protect the privacy of children and be safe from "physical or mental violence." But it focuses on the child.
You can think of many reasons why the U.S. has not ratified this. It covers both issues. We helped draft it. But then refused to ratify it. Partly because some states allowed kids to be executed. It also makes closed adoptions a violation of a child's rights, especially if they are adopted by a different culture. (I agree).
Children in the U.S. have the fewest rights of any reasonably developed country on this planet. They're property even though it's not legal to actually sell them (but there are loopholes, look at adoption costs).
I do believe parents should have certain rights to protect and raise their children, but as you mentioned, a lot of parents range from kinda shitty to outright abusive. So we do need to protect children from their parents if needed.