I can't offer specific routing advice, but just some pointers. Consider luggage requirements, and also connectivity at airports. That is, if you book with two different airlines, just remember, if one is delayed, it then may be up to the good will and nothing more, for the second carrier to put you on a later flight. This can be avoided using a good agent.
If you are taking a break, one routing that can be good, is via west coast USA, at that time of year, you can go via San Francisco (VS to LHR, then NZ (I think?) to christchurch), also via LAX (but most FF pax prefer SFO, as it's a tad more civilised). One cool aspect (depnding upon how easily entertained you are), is that if you spend a few days on the west coast USA, then flying to NZ will give you very little jet lag, as there are only a few hours time difference, but, and heres the good bit, you will lose exactly one whole day from your life (as you cross the international dateline) - the opposite of what happened to phileas fogg.
Anyway, I'd highly recommend a good specialist agent, as they can put several flights together for you, on one reservation, check your travel documentation for you, and maybe suggest a really unusual stopover as well. As some have said, trailfinders can do it, but also travelmood are especially good at flight routings to oz and NZ.
Also think outside the box, maybe it's cheaper to fly to Western Australia (Perth), and then use the budget airline Virgin blue to connect via adelaide or sydney to christchurch
Finally, not sure how good this is with kids, but have you considered a 'round the world' ticket. These can sometimes offer a real cost saving, and are often completely changeable, with one or more stopovers each way (up to you) and again a specialist agent will know these tickets inside out. All the main airlines offer these, including the alliances, like oneworld, star alliance etc. If you only want to make a single stop each way, then virgin and NZ do a combined round the world ticket. One point though, if an agent tries to 'push' you with one airline only, then they are probably getting a good kickback. A good agent will provide you with multiple options. Don't take the first prices, check with another agent.
Don't forget, if you fly all the way to NZ, it might be worth spending a few days in Wellington, then catching the overlander train down to christchurch from picton, via the whale watching town of kaikoura.
Oh, and if you end up stopping over in Hong Kong on the way back, don't forget, that the chinese new year fireworks there are the best in the world - and you might just make it, as in 2009, it falls in late January.
Hope that helps. Oh, final tip, sometimes it's worth busting the bank a bit for a trip like this.