neither is nz. OP has some rethinking to do.

I do know people who are semi-retired or part-time students who choose to live in China for the low cost of living but children would complicate this enormously. As others have pointed out, International schools are horrendously expensive.. Home schooling is an option.
My research suggest a couple of options: New Zealand, Hawaii, South America ? I am not sure these countries absolutely mirror the school schedules in the states.
Besides the obvious....South America is not a country. Are you a friend of Sarah Palin? South America is a continent. Hawaii is one of the 50 states of the US.
You must be a troll!