Your children will need a student visa each.
http://www.immigration.govt.nz/migra...iningmyfamily/ You fill in the form as if you were the child, then you sign on their behalf at the end, as their parent.
Your wife will need to apply for a partner-sponsored temporary work visa.
http://www.immigration.govt.nz/migra...milystream.htm The word 'work' in the title does not mean that she has to have a job at all, but that she is allowed to work if she wishes. This could be at any job, and doesn't have to be skilled, because this is an open visa, not restricted as your work visa is.
You can send off these applications all together, linked with a covering letter to your work visa application, then they will be processed as one case, and the CO will supply information you won't know at first, like your own visa number, as it becomes available.