Getting your bags off your domestic flight, and walking from from the domestic terminal to the international terminal should take no more than 30-45 minutes, so if the goal is to check in on time for your international flight, 3 hours is usually fine.

BUT, this assumes your domestic flight is on time. I flew CHC-AKL two weeks ago with two people connecting to SFO. Their itinerary allowed them 3 hours but weather meant their original flight was cancelled and their flight with me (1 hour later) was delayed by 2 hours. The result was a lot of stress and, ultimately, a missed flight.

Personally, I suggest you travel to Auckland in the late morning to take the stress out of the day. Flying on two separate tickets means you are responsible for any issues caused by delays, with little or no help from Air NZ.