I want my children to attend a New Zealand school and I wish to be with them in New Zealand.
Your child may be eligible to apply for a Student Visa as an international student. As the parent, you can apply for a Visitor Visa in order to care for your children while they study. This is called a Guardian Visa. However, it is unlikely that the other parent of your child can come over as well, because only one person can get a Guardian Visa for each family. This is the case no matter how many children come over on Student Visas.
When you apply, you must show that you have NZ$1000 per month to cover living expenses, for the entire time your child is enrolled to study on the Student Visa. This reduces to $400 per month if accommodation is paid for in advance.
It may be possible for you to work part time from 9.30am – 2.30pm (Monday to Friday inclusive) but you must first apply for a variation of conditions of your Visitor visa to allow this.