There are English-language requirements for children who are 16 or older (including 16), so your children would not be required to show their English-language skills.
At what age do language requirements begin for children on a New Zealand investor visa?
My wife and I are interested in the New Zealand investor visa program. Our 7-year old is fluent in English and we are confident that he will meet the language requirements. We also have a 9-month-old daughter. How would the language requirements apply to her? Is there a certain age at which she would be tested?
Principal applicants under the investor 2 category must meet a minimum standard of English, which is either a result of a recognized English test, such as an IELTS score of 3, or an English-speaking background that satisfies the immigration officer. Any partner or dependent children 16 years and over who are included in an investor 2 category application must meet a minimum standard of English or pre-purchase ESOL tuition (see BF1.1).