I would suggest you have a long family holiday here and have a good look at whats here for you.
From my experience children are happy to try new places and new things but you do need to share your thoughts with your family.
Sit your family down, do some proper research about areas, what do you want in your life and where can you experience it in the uk etc
Most of the crap you read about 'how terrible the uk is now' is utter rubbish. Newspapers print all sorts of crap that everyone just seems to believe without it actually having any effect on them personally, yet they're happy to trot it out as fact to anyone who will listen.
Have a proper look at jobs and areas you might want to live. I would recommend areas with several schools rather than just 1 school to choose from (rightmove has a 'schools in the area' type thing when you view a property) or be prepared to travel to school. I do an 8 mile school run to access a slightly massively better school for my dc .
I would guess if you own a home in NZ that you will have a reasonable amount of money for a UK house given how expensive it is in NZ so you will probably have more choice than many first time buyers in the UK.
If you can avoid the SE and London as those prices are stupid prices for houses and rent. Unless of course this is where you want to be.
I think you should give it a go. I would hate to be living in another country purely on the basis that its keeping someone else happy.
Why does it always seem to be that Mums have to put up with being miserable and unhappy and none of those 'happy people' ever want to consider living anywhere else in case it makes them sad..........just like Mum is ? 