"A child has very few rights until they reach 18 years old. the parent's have rights over the child, as long as they do not break any laws. No freedom of speech, no freedom of assembly, no freedom to arm themselves, etc..."
So a child under the age of 18 has no freedom of speech or freedom of assembly and they can be searched without warrants? Au contraire, my friend. The Constitution affords those legal rights upon every citizen. The government has put certain limitations upon it, but did not strip them. A person under 18 can possess a gun in many states, they just can't buy it themselves.
You also raise the point that the parent's have rights over the child - this is true. And so if the father decides that his daughter can handle a loaded firearm, that is his decision. And further, there are no laws saying that you can't let a son/daughter handle a weapon while the adult accompanies them and permits them. So a father in the house giving his daughter a handgun, no matter what age, is not illegal, despite how stupid it may be.
-Devil's Advocate, signing off!