WK2.5.15 here.
https://onlineservices.immigration.g...nual/45676.htm
Your partner can apply for a partner-sponsored temporary work visa, to match your ESV for length of time.
https://www.immigration.govt.nz/new-...k-visa-holders
Your children can apply for student visas, likewise to match your ESV for length of time.
The family applications can go in at the same time as yours, linked with a covering letter, and INZ will work them all as once case, supplying information you won't have at first, such as your visa number, as it becomes available.