Ah, that blessed spanner at work again! Someone will have to lock it in a cupboard out of harm's way, although I'm sure Beth is happy with the way her spannerism worked out.
Nicky, as Beth says, you can start your PR process now. At least it would be under way. If your hospital will bring forward your start date to the near future, you could apply for a
WP to get you into NZ and into work. With this, your family can also get in off your back and your kids should be able to get Student Visas, which means you wouldn't have to pay international fees although it's not straight forward for tertiary education if Jenni is coming with you.
A dependent child of someone who holds a New Zealand work permit will be regarded as a domestic student for primary and secondary school, so will not need to pay international fees. For tertiary education, however, your child will need to meet our general requirements as an international student, including paying foreign student fees.
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.
Your WP could run alongside your PR application and you just switch over when the PR comes through.
If you go the WTR route, you would have to work for 2 years before you can make the transition to PR.