Legal Question in Family Law in California

That's a big maybe. Japan is one of the countries that regularly refuses to enforce U.S. custody orders. I don't know how that would play out on a U.S. military base. I would not count on it if my children were involved. I strongly recommend that you not consent to the children leaving the U.S., and if necessary obtain orders for the childrens' passports to be deposited with the court, until you can sort out exactly what will happen and how to protect your custody and visitation rights if the children leave the country.