Hey, pleased you can make to NZ, is this your first time? At first I thought you must be going to stay in camping grounds, if you are renting a camper van this would be the cheapest accomodation considering the camper van is also your travel. If you are traveling in the the camper and also staying in motels then this must be the most expensive.
Some of the backpackers are really good for familys, sheared kitchen etc but your kids might think thats fun. It might be cheaper to rent a car and stay in cheap accommadation, ie backpackers.
The ferry crossing is expensive even for a small car $300+nzd, a camper could be double.....I,d think about ditching your car/ camper in Picton and get another one in Welly.
Things to see, Gueenstown is a great place to start. Fox or Franz glasier would be a good next place to go, then drive up the west coast of the the south Island, (maybe stay a night in Hokitica or Greymount) the west coast is very laid back and theres a pub on every corner.