@Ron Gibson
It sounds as though you have done a lot of work on this already - and the MOST important thing that you have decided upon, is to take a couple of days upon arrival, to settle down/'de-compress' after the long flight/multiple time zone changes. Many have fallen asleep at the wheel of a camper van hired right off the flights. Very sad outcomes.
Your original question seemed to be about flights. If you are not a frequent long-haul traveller (7-10 hours plus), then this is probably the most important part of all of your planning - and a cheaper fare isn't going to help you when it involves 16 hours on a single flight (Qatar Doha-Auckland), or almost as long on Emirates (Dubai-Auckland).
My advice: see if you can get yourself on Singapore Airlines (
www.singaporeair.com) with a 2-3 day stopover EACH WAY in Singapore. The Web site is very clear in laying out your flight options and corresponding pricing... These can vary even on the same day. The airline offers some great 'Singapore stopover rates' and if they don't suit you, have a look online to book direct at somewhere like Holiday Inn Express Katong (see:
www.ihg.com and sign-up for membership rates). Feel free to PM and I can give you some more hotels to consider.
The principle advantage of Singapore Airlines is that their crews look after you. And this route breaks up your flights into easier-to-manage sections. Plus you can take an overnight flight from Heathrow (they have others).
Good alternatives for mostly the same reasons are Thai Airways via Bangkok, or Malaysian Airlines via Juala Lumpur (again, with stopovers).
Important: make sure that you get sleep on the plane on the London/Singapore sections... Don't spend all flight watching movies and arrive exhausted! Sleep is the single most important factor to manage jetlag. (Again happy to have a PM session for more insight into flights).
In N. Z., others have covered much of this and I agree about flying back from Christchurch... But you would do well to just fly into Wellington and then take a few days with a rental car to drive up the west side of the North Island, via New Plymouth, back to Auckland.
February is good timing: weather is generally very settled and warm (humid in Auckland), kids are back in school, days still reasonably long.
Just do remember in terms of personal safety and the security of your property:
N. Z. has jails, too, and they are also full. Petty crime that sustains an out of control drug scene is a real problem that ruins many holidays.