How did New Zealand's continental crust get split between two plates?
The continental crust and shelf of new zealand is one peice that has a fault running through it due to it running over a boundary between two oceanic plates. Continental crust cannot really* subduct due to its lower density so if forced onto a subduction zone they will actually slide over it onto the other plate. It helps of you remember oceanic crust and continental crust can exist on the same plate but have different properties. 

Something similar has/is happening in North America the san andreas fault is caused by part of the north american continent running over the old east pacific (farallon) plate and spreading center, so now the portion attached to the north american plate is being dragged in one direction and peice sitting on/in the (west) pacific plate is moving in a different one. it is slowly pulling the continent apart and eventually may create an island like new zealand. 

Here is more in depth discussion of strike-slip/transcurrent plate boundaries. 



*small pieces can get dragged down but not much.