I found this on the INZ Operations Manual.
E4.5 Spouses or de facto partners and dependent children of student or work visa or permit holders
Spouses or de facto partners of student or work visa or permit holders may be issued with temporary visas or granted temporary permits of a type appropriate to their needs for the currency of the spouse or partner's visa or permit.
To be eligible for a temporary visa or permit, spouses or de facto partners must be in a genuine and stable relationship*. For de facto partners the couple must also have been living together in a genuine and stable relationship* for at least 2 years immediately before the application is assessed.
Dependent children* of student or work visa or permit holders may be issued with temporary visas or granted temporary permits of a type appropriate to their needs for the duration of the parent's visa or permit.
Spouses of full fee scholarship students, who receive a 'dependant's allowance' from MFAT, require MFAT's approval to be granted a work permit.
It confirms that you can get a WP of your own. Your children can be included in the application and I know that older children are granted Student Visas. I'm not sure what happens with very young children but I'm sure that has to be a way of including them because it says....
Dependent children* of student or work visa or permit holders may be issued with temporary visas or granted temporary permits of a type appropriate to their needs for the duration of the parent's visa or permit.
From
here .
I'm sure it will be OK for all of you to get in.
And yes there are a lot of British people on this forum but also many other nationalities. Some of them don't hang around very long and just ask their questions and disappear until the next questions arises so you aren't always aware that they are part of the forum.