campervan is not as idyllic as you think - March can be coolish at night and there is never a guarantee of no rain. That said, with small children the campgrounds are ideal, you won't be welcome in most hostels. Where you WILL be welcome is in motels which in NZ often have full cooking facilities.
NZ is about the size of the UK and driving ALWAYS takes longer than you think - google maps often gets the estimates half what they should be.
lovely beaches but you may find things cooling in March, also be aware of the sandflies which don't show in the photos! Also you can see and play on beaches a lot closer to home. I wouldn't build an NZ trip round beaches.
I have to disagree with some of the recommendations here. For instance, the LITTLE blue penguins don't appear until dusk so you can't see them! The yellow-eyed ones keep much more user friendly hours and can be seen from the distance you need to keep. I also don't think the multi-day hikes are at all practical with small children.
so how about this for some ideas. (not really in any order)
- arrive Auckland, couple of days there to get over jetlag when you shouldn't drive anyway. South to Rotorua (four hours) for lots of smelly volcanic stuff. While there is loads more to see on the north island I'd recommend the south for the rest of your trip for the real see-nowhere-else stuff. If you do want your NZ history, the Bay of Islands is the place but as noted it will bore the kids.
then fly to Queenstown and base either there or 90 mins drive to Wanaka which has a Lovely lake, play areas, little walks, Puzzling World.
perhaps Te Anau (Queenstown 3 hours). Beautiful lake, bird park where you WILL see the NZ bird life. Not sure about Milford Sound with toddlers but if you do the trip, do it from Te Anau NOT Queenstown.
I'd suggest south to the Catlins for wildlife - sea lions, yellow-eyed penguins, maybe dolphins. Then on to Dunedin where you will see the sea-lions at Aramoana, and the historic Taieri Gorge train ride might also be a hit. And yes, the chocolate factory. Call me a big kid but I loved it... Oamaru is indeed fun and very different with its whitestone buildings.
the glaciers are isolated on the west coast and it is a long drive from any of these places. You can't take kids that small on the glacier but you can walk to near the Fox glacier at the moment. BTW never feed keas! Check current status and remember it rains 2 days in 3 on this coast.
I also think Golden Bay is lovely, and you can go up to Farewell Spit for more wildlife. In between the two (glibly dismissing some LONG drives) there is Hokitika which has a Kiwi centre, the only way to see these nocturnal birds. There is also a glow-worm cave on the road outside the town, and it has a great pebbly beach (not swimmable though).
bit random here but hope it gives you some ideas. I strongly suggest getting the Rough Guide to NZ (the lonely planet one isn't very good)