Maybe Okinawa Prefecture knows how such official records have been handled.
The family register system of Japan was drastically changed in 1948. And, after the occupation was over in April 1952, Okinawa was under the control of the U.S.A. until May 14, 1972.
I'm not sure which division of Okinawa Prefectural Government is the best to consult on your question, but Municipal Administration Division sounds to be a near guess.
http://www3.pref.okinawa.jp/site/view/cateview.jsp?cate...At the bottom, above gray and blue lines, are a phone number, a facsimile number and an e-mail address to this division. Below the lines is an e-mail address to Okinawa Prefectural Government.
You don't need to reveal real names until an opportunity comes to access a record.
As to phone calls from abroad to Japan, this page offers a brief explanation.
http://www.japan-guide.com/e/e2223_how.htmlI suppose, when your grandmother was / is a Japanese national will make differences.
If she was no more a Japanese national after that marriage, I think it's hard to find clues on Japan side.
As Uco suggests, it's highly possible that her family register domicile ([honseki-chi]) was / is located in Okinawa.
Events such as marriage and childbirth, if confirmed on Japan side while she was a Japanese national, must have been recorded on a family register ([koseki]) to which she once belonged / now belongs.
If any of the six children was born while she (= your grandmother) was a Japanese national, and also the child was once / is now a Japanese national, then maybe the child belonged / belongs to the same family register as she.
However, Japanese local service officers will not easily open this very private sort of official records, because they should prevent abuses. (If there is her Japanese near relative in Okinawa, possibly it's easier for them to indentify the relative on Japan side.) If you fortunately find official records concerning her on both Japan and U.S.A sides, that might be a chance to form a clear picture.
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