Funny, my parents did something very similar when we kids were the same age. They hired a camper van which I'd recommend for you also - the south island is pretty slim pickings for public transport, especially when you've got the added complication of wanting to get out in the wilderness for some adventure. That way, you get accommodation AND transport sorted in one easy swoop!
General advice is to stick to nature and avoid cities as much as possible (although Christchurch is nice in my opinion - there's a good art gallery there). This seems to be a good site for ideas on where to take your kids:
http://www.kidzgo.co.nz/You're set for adventurous activities in NZ, the problem will be deciding what and when - probably best to check local operators at the places you end up visiting. Queenstown is the main centre for 'adventure' activities, but it ain't the only one. This link should help your wife with some ideas:
http://www.newzealand.com/travel/about-nz/...events_home.cfm In fact, the entire Official NZ tourism site should probably be your first stop - they have a good spread of maps, destinations, events and accommodation listed, and a travel planner so you can save details to come back to.
You'll get much better advice if you come back here with an idea of an itinerary rather than asking someone here to provide you with one. First, it makes us feel like you're using us as free travel agents, second you're the best person to decide what's going to excite your family and you most - then we can help you with the practical questions
