I have never been to NZ, so I am not discrediting the country, just urging you to think carefully.
It is an enormous undertaking to move from one country to another with a family.
You want family life, but you will be uprooting your family FROM all the family you have, and become a single isolated unit somewhere very far away.
You will be immigrants. You will come to a country where you might not even know how things work, with mot, car insurance, signing up with doctors, home insurance, home buying and renting, it may all work very different to what you are used to.
I moved my family back to my native norway last year. It has not been all rosy, I can tell you that much. Norway was not to me what I thought it was, and things are very different to how I thought it would be. It has taken a year to get used to how things work here, and I am still not used to all the details. I left when I was just 20, so had never really been an adult here, and I realize it is very different from the UK. I miss England nearly every day.
The life you picture, is possibly the life we have now (but in a much coldre climate), and when you have stopped being in awe at how fabulous it is, reality creeps in, and you think back to what you had, and you might miss it.
Dh has not really settled here, and he is unhappy with life in general here, so I suspect we will be back in England within the next few years.
We had no family in London, and although it was hard going at times, it was doable. We led perfectly happy lives without grandparents and the support they could possibly offer.
The kids are very happy here. We have a big garden, live backing onto the woods, on the side of a mountain with alpine slopes "in our back yard" - it is literally just five minutes walk from our house to the lifts. Our 7 year old is now very good at down hill skiing and cross country too. He plays out with the other kids in our street daily, most of the time I dont really know where he is, there are so many kids he could be with. He walks to and from school on his own, and has responsibility and independence we could never dream about in London. He does not want to go back and loves it here.
You can get "the new zealand life" in Norway, and it is only 2 hours away by plane.
Whatever you decide, good luck!