Why does a child custody order have noting to do with children rights only fathers rights?

Why does a child custody order have noting to do with children rights only fathers rights? Who is right if the Japanese mother has a Japanese child custody order over her US born children in her favor and is in Japanese with her children, but the American father has a US child custody order in his favor? Basically both American & Japanese child custody orders are in conflict of each other.
Some say that a child is considered personal proparty of the father untill age 18, is that correct, yes or no?

The mother would keep the children in Japan with her. It would be illegal for the father to take them out of the country.