"This is a very sad case for which there is no ready resolution," wrote Justice Murray Gilbert in giving the reasons of the appeal court.
"While we are satisfied that a return order should have been made in 2017, we cannot overlook what has occurred in the two years since and ignore Anna's consequential present fragile state and vulnerability."
In a separate part of the judgment, Justice Forrest Miller went further, to say he "reluctantly" agreed with his judicial colleagues.
"This case is a striking example of the sort of self-help behaviour that the [Hague] Convention is intended both to discourage and to remedy. As at the date of the Family Court hearing, all criteria for decision pointed to return," wrote Justice Miller.
"However, I accept that the unhappy combination of delay in rectifying the error made in the Family Court and the father's decision to take matters into his own hands allowing the Family Court hearing has made a difference."
"Taking matters into his own hands", as Justice Miller described it, was when the father took Anna from her classroom with the help of an Australian "child recovery team" following the original ruling of Judge Coyle in the Family Court.
The father said he took the extraordinary step to re-establish contact with his daughter, whom he had not seen in nearly five years, after his former partner secretly took her from their homeland in Europe.
And the only custody order in place for Anna was the one issued by the European court, which noted the mother's conduct showed she would not release her daughter without "direct force".
The consequence was his daughter considered her first meeting with him in years as an abduction and now suffered post-traumatic stress disorder.
"I was shaking so much, I was scared. They just took me, I thought I was going to die," the girl said, according to the report of an expert psychologist which was read to the Court of Appeal.
The decision was "extremely unwise" said Justice Miller in the Court of Appeal hearing in July.
However, despite the setback in the Court of Appeal, the father now plans to lodge a final appeal with the Supreme Court.
The mother declined to comment to the Herald, but will consider an interview at a later date.
The man, who represented himself, was disappointed he successfully argued against the two legal points on which the Family Court refused to return his daughter, later upheld in the High Court. Yet the final outcome was the same.
"All I want is to be part of my daughter's life and a child needs both parents," he told the Herald.
He recognised his daughter would not be able to live with him without her mother, so had proposed a joint custody arrangement in Europe.
If his daughter was not returned, the father said New Zealand would become the destination of choice for parents who choose to flout custody orders in their home country.
"There is a risk you lose a case in one country, you come to New Zealand and get another chance to win."
If the girl is sent back to Europe, her mother has said she will stay in New Zealand with her new husband and their youngest child.
The psychological trauma she would suffer as a result of being separated from her mother, step-father and sister was a significant reason for the girl's strong objection to being returned to her father.
But Justice Miller was openly sceptical of the mother's claim she would not follow her daughter back to Europe.
He also noted there is no guarantee the family could stay in New Zealand, given their temporary immigration status.
The only reason the family were granted a reprieve from deportation was because of the original Family Court decision, which was wrong according to the Court of Appeal.
The ruling of the three senior judges is the latest legal twist in a "unique" legal case first reported by the Herald in 2017.
For two years, the man had no idea where his daughter was living until a social media campaign to find her went viral online.
By chance in late 2016, someone recognised the child in New Zealand, where the girl and her mother had started a new life.
The father tracked them down and asked the Family Court to return the girl to his home country under the international child abduction agreement, the Hague Convention.
Judge Stephen Coyle - despite accepting the mother unlawfully took the girl and concealed her - refused to make the order because she was now settled in her new country.
She also strongly objected to returning to the country of her birth.
Sending her back to her home country would be an "intolerable situation" and "cataclysmic" for the girl, said Judge Coyle, and returning her was not in the child's best interests.
His ruling on the Hague Convention application was upheld on appeal to the High Court last year.
"The predictable effects of an order for return are much more than tears and mere physical and emotional upheaval," Justice Paul Davison wrote in June 2018.
"Here the effects of an order for return will be harmful and damaging, with potential lifelong consequences."
But the High Court judge pointed out his decision should not be taken as condoning the mother's actions, which he described as an "egregious breach" of her legal obligations.
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Generally speaking, the deterrent provisions of the Hague Convention are in place so the "abducting" parent should not gain an advantage from concealment or deceit.
But because the father did not know where his daughter was for two years - because of concealment - this meant the mother could rely on the "settled" defence to keep her daughter in New Zealand.
Justice Davison said she was taking advantage of her unlawful conduct in "flouting" the court orders in her home country.
"The respondent's reprehensible actions are the very kind of conduct that the Hague Convention provisions and policies are directed to prevent, and which the courts of all jurisdictions rightly condemn as contrary to the rule of law," said Justice Davison.
"It is important to keep in mind that throughout that extended period, the [father] has been prevented from having any contact whatsoever with his daughter, while the [mother] has had exclusive contact and the opportunity to influence Anna to adopt her attitudes towards the [father], rather than Anna forming her own views independently."
Despite this, Justice Davison ruled Anna's welfare and best interests outweighed the Hague Convention policy provisions.
In July, the case was heard afresh in front of Justice Christine French, Justice Forrest Miller and Justice Murray Gilbert in the Court of Appeal.
The father, who flew from Europe for the hearing, argued the case himself without a lawyer.
While not strongly challenging the finding his daughter is now settled in New Zealand, the father disputed how Justice Davison balanced the competing interests.
He submitted not enough weight was given to the deterrent purposes of the Hague Convention, or the concealment of Anna following her wrongful removal from their home country.
Immigration New Zealand wanted to deport them because the mother gave them false information for the visa, although they have since been granted a reprieve.
For his part, the father has said he is willing to share custody with her mother.
Alex Ashmore, the lawyer representing the mother, said the daughter's opposition to leaving New Zealand was not solely based on her belief she would be separated from her mother.
The girl considers herself a Kiwi and enjoys her life with friends and school in New Zealand, while associating her country of birth with conflict between her parents, said Ashmore.
Ashmore said he could not excuse the mother's actions.
"When you look at the file, you think that's not fair. Why should someone be rewarded for hiding?
"But at the end of the day, Anna didn't hide. Her mother did."
The courts in their home country awarded sole custody to the father after the mother repeatedly refused to let him see their daughter.
"The ingrained resentment the mother holds against the father, now significantly impairs the mother's ability to raise her daughter ... with her actions, the mother wilfully and significantly disregards the interests of her daughter," the European court judgment said.
The girl's mother has claimed in court documents the custody battle was "vexatious" and "relentless harassment" which made their lives "unbearable".
Justice Miller noted the European courts never issued a protection order against the father for the alleged "stalking" and said it was unsurprising the father would try to maintain a relationship with his daughter.
"She kept moving, he followed her around," the judge said. "One of the difficulties with this case is the mother has gone to extraordinary lengths to do exactly what is not in the best interests of the child."
And despite who was right or wrong, a leading family law expert said the Hague Convention was for the benefit of the child - not the parents.
Margaret Casey, QC, was representing the Central Authority, part of the Justice Ministry, which administers Hague Convention proceedings in New Zealand.
She said Anna's case was "particularly unique", even internationally, because it featured concealment of a child who was now settled.
"Concealment is at the heart of the Hague Convention. This is exactly the kind of case. The question is what do you do with the other side of the balancing process," said Casey.
"Essentially this court will be asked to weigh her tears against the tears of children who may yet be abducted. All those children out there who need to be protected."
Global custody battle
• February 2017: Application lodged with Family Court to return Anna to her father in their homeland.
• May 2017: Immigration NZ issued deportation liability notice against mother for concealing relevant information in visa application.
• September 2017: Family Court rules girl should not be returned to father in homeland.
• October 2017: Immigration and Protection Tribunal cancels deportation notice and issues new visas.
• June 2018: High Court releases full reasons upholding the decision of the Family Court.
• July 2019: Court of Appeal hears 'particularly unique' case which raises difficult balancing exercise for Hague Convention.
• November 2019: Court of Appeal finds Family Court should have returned Anna in 2017, but ruled against overturning the decision because too much time has passed and she is now fearful of father.