[Nyororin]

I am going to second the suggestion of different area / different school if there was definite bullying happening. But to be honest... Second grade is really a bit early for any real bullying. Out of school activity at that point makes far more a difference than in school interaction when it comes to the number and closeness of friends. It is only later that children are really able to make and manage friendships on their own... It sounds like you left Japan before that stage, so your concerns about bullying may have been unfounded. It is very hard to compare the difference in school life and friends at one grade level to another as the social capabilities of children change so much over time... So more friends years later in a different country and different school doesn't mean that she wouldn't have had more friends and been more relaxed in the same school in the same country after another year or two - or even in a shorter period with more community involvement, etc.
I suspect that your daughter's reluctance is based far more on her current friends and school experience than on negative past experiences. What child wants to leave friendships at that age?

If you were much happier living in Japan, I say to go for it. A happy home life is something that should be be given priority. If you are stressed and your wife is stressed, it is only a matter of time before the kids are stressed and the marriage itself becomes stressed. I would choose the possibility of issues at school over the definite of an unhappy home life.