NZ is different to OZ in these cirumstances. You can apply onshore and
be granted the visa onshore.
The only real problem I see is one of timing of visa grant in relation
to the childrens schooling.
If the visa (or more correctly the permit) is granted pre the new school
year - no problem.
If NZIS take longer to process the application you could run into
problems enrolling the children into schools. I have however seen
some good old kiwi common sense applied by headmasters knowing that a
permanet residence is on the way!