The reality in the US is a mother can move across the country while a father is forced to pay child support, if he moves he can likely lose his well paying job, and if he can't find a just as good job where he moves he could be put into jail for non-payment (debtor's jail!).
The reason we haven't signed the Declaration for the Rights of the Child is because the areas it addresses is a state issue. If the Federal government were to sign such a treaty it would become law. Which is a big no-no since the federal government can't intrude on state issues.
Could we have a referendum on the issue at the federal level, or would it require the states to individually ratify (through state governmental bodies or referendum) the right of an agent of the federal government to sign the treaty and allow it to become state-level law somehow?
I don't know much about law, but I am a fierce advocate of state rights based mostly on the idea that it is far more feasible to have a democratic government that involves millions or tens of millions than one that involves hundreds of millions. This issue is however one place where my ideas trip up. It is kind of embarrassing that we are 1 of 3 (assuming the grandparent comment is correct) countries not to ratify the treaty and the other two are an (essentially) failed state and a brand new one that has to sort its internal self out before working on such things as UN treaties.