I too was a child that moved a lot - like Andi 18 times by the time I was 18. It was really hard especially since I never felt like I belonged anywhere.
My move from English Toronto to French Montreal was the hardest - culture shock and language barrier all at once on top of all the other issues I was dealing with. I didn't do well at all.
If she has supportive loving parents she will do OK. Since she has a Japanese father she will be attuned to some of the culture already so that will make it a lot easier on her too.
Perhpas getting books from the library for Jennie and her friend to go through; or finding some recipes they or you could make, or traditional artwork. Little things that help to make the unknown more familiar. Maybe even learning a few words in Japanese would be fun and encouraging.
As for you Nina - yes the old memories get triggered. Think of what would have helped you back then and do it now for yourself.