I think one thing that could help would be continuing to do things with the family that aren't culture specific, things that you did in the US. Like going the park. Also, maybe there are local organizations made up of other non-New Zealanders that plan group activities and outings.. that way, you get he best of both worlds: other Americans who're in the same boat as you who are exploring their new home too. It might be easier to make the transition in a larger group, especially the kids, who might meet other kids.