There are a few new pieces to the puzzle:
Father, kids in custody case Japanese citizens, officials say - CNN.com
Apparently the father had been living in Japan for quite some time (I guess you can not get naturalized through marriage alone?), and had stated a permanent address in Tokyo. And they never had divorced in Japan, only in the USA.
Unfortunately it doesn't say how long they actually lived in Japan as a family/how long they actually lived in the USA. That would be something really interesting,and big part of forming an opinion about the case for me personally.