My brother and sister-in-law did a similar thing last month. They were flying UA JFK-SFO, connecting to MEL via AKL on NZ7. UA couldn't check them in all the way in JFK (bags yes, BPs no) and they thought they might be able to do it all when they arrive in SFO, and spend the rest of the day in SFO. Turns out, NZ checkin wasn't open, and wouldn't till a few hours before the flight, so they had to be at the airport again at regular checkin time.

good luck
goodo