Hi, I know one family (2 adults, 2 kids) in South Island who lived in 16 ton well setup campervan bus for 8 years, while saving for house. They said it was the greatest time in their life. Their home bus, when automatically unfolded was like 40 square meters, included kitchen, washing machine, etc.. We lived in 30 square meters flat with 1 kid, before moving to NZ, and it was manageable. I would probably enjoyed more 40 square meter bus instead, if I had one at that time. It is certainly possible and not that inconvenient as many think. If you can get used to the regular cycle to go to the dump station and home school your kids with the help correspondence school (which is in Wellington, BTW) and live in a bit smaller space, it should be fine. Home schooling kids is actually a good idea, as you can teach them a lot more than schools teach nowadays (at least until High School time).
Regarding rate payers paying for you. Ignore these comments. There are so many people in our society who live in social flats / houses, paid benefits and live on this without thinking to do something about. Your intents are to get off the ground and good on you. I support this idea.
Regarding space available for camping grounds. You need to make sure you reserve the space. And if you are late and it is all occupied, in Wellington, you can park on a side road with free overnight parking (that is what Park Ranger told me). There is no difference if a vehicle is parked free or if there are people inside of it and what they do just reading or sleeping. To make it easy and convenient for you, make sure your van can do complete black out hiding, so people around have no clue if you are in the van (watch youtube about this, it is very much possible). Also install a security alarm, so you wake up when somebody attempts to break into your van. And I would ignore people who complain there is no enough space to go to holidays. Well as you can see there is no enough remaining land to just live, all land is sold and requires a lot of money to get your spot on the Earth. So, you take what is available to live, which is far great intent than to keep the free land for somebody wanting to go on holidays occasionally.