The move to New Zealand was only supposed to be for five years but after the marriage breakdown, the mother decided she wanted to take up a lucrative job in Melbourne.
The father, a beneficiary, objected and the Family Court agreed everyone should stay here.
But the mother appealed to the High Court, and it granted her permission to travel, with Justice Graham Lang ruling that relocation was in the best interests of the children.
Among the conditions he imposed were that the mother must pay $25,000 into a bank account so the father can use this to either move to Australia or for his travel costs when visiting.
She had also arranged for the father to stay at her parents' home when he was visiting.
After a court hearing, Justice Lang said the mother's employment offer would be terminated if she stayed in New Zealand for much longer.
The father's lawyer said Justice Lang had put the children's welfare second to the job offer and that it was in their interests to stay in New Zealand.
He applied for a "stay of execution" so everyone would remain here for now but, in a ruling issued this week, the Court of Appeal disagreed. The appeal judges said the father could still fight for custody if the children were in Australia.
"[Justice Lang] has made very detailed orders providing for the applicant to have generous contact with the children whether he stays in New Zealand or decided to move to Melbourne," the ruling says
"[The mum] has significant qualifications and experience ... and she has the opportunity to take up part-time employment in Melbourne with substantial remuneration. Contrary to [the dad's lawyer's] submission, the judge did not take this factor into account at the expense of the paramount consideration of the welfare of the children."
Only at the last minute did the father suggest an alternative - that the mother takes home the youngest child and leaves the rest here.
The Court of Appeal ruled that out. "Obviously it would have the effect of splitting the family, which is not in the interests of any of the children."
Otago University family law expert Professor Mark Henaghan said the decision seemed "pretty straight- forward".
He said the mother's funding of the father's travel and accommodation was "unbelievable".
"She couldn't do much more."
Professor Henaghan said New Zealand and Australian Family Courts worked well with each other and there would be no problem returning the children to New Zealand if necessary.