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.
But the Family Court - despite accepting the mother unlawfully took the girl and concealed her - refused as she was now settled in New Zealand.
Judge Stephen Coyle said returning to her father would be an "intolerable situation" and "cataclysmic" for the girl, who now considered herself a Kiwi.
The ruling was made even though the girl and her mother may now be deported.
The Family Court ruling has now been appealed to the High Court by the frustrated father, who said authorities in his country may also try to extradite his former partner.
"All I want is to be part of my daughter's life. A child needs both parents," he told the Weekend Herald.
Yesterday, the girl's mother politely declined to comment, on her lawyer's advice, when approached at her home.
"There is an ongoing court case and we want to make sure that we protect our children."
The father is at a loss to explain why his former partner went to great lengths to cut him out of his daughter's life.
The courts in his country awarded sole custody to him 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.
Several years ago she travelled to New Zealand with their daughter.
Together, they started an "idyllic life" and the girl was enrolled in school.
"During this time [the father] had no idea where his daughter was," said Judge Coyle.
"Through a coincidence, in part helped by an extensive media and internet campaign...he was alerted to the possibility that [his daughter] may be in New Zealand."
In December 2016, an application under the Hague Convention was made to the Family Court which ordered the surrender of the daughter's passport.
The mother accepted she had unlawfully taken the daughter, but asked the Family Court to refuse the application on several grounds.
One was the girl was "settled", physically and emotionally, in her new community.
She was having music lessons and also involved in a range of other school activities.
"Totally happy to be a Kiwi girl, loves the outdoors, enjoys the environment," the principal at her school was quoted in the judgment.
"She is just amazingly well adjusted, she is neat, I wish we had more [students like her]."
Judge Coyle agreed she was settled, despite a potential deportation clouding the issue.
Mother and daughter have been served with deportation notices by Immigration New Zealand, because she did not tell the truth about the custody arrangements.
She has appealed the decision to the Immigration Protection Tribunal, although the Family Court was told the chances of success were "minimal".
But Judge Coyle said he could not take the immigration issue into account, despite accepting it was "more likely than not" the appeals will fail.
"I have to make my decision based on the basis of the known evidence before me at this point in time," Judge Coyle wrote.
"If [the girl] subsequently leaves New Zealand because a decision is made to deport her parents, then that will come to pass."
In awarding custody to the father, Judge Coyle said the overseas courts ruled he was not a safety risk to his daughter.
The Appeal Court in the country also found the mother had an "ongoing lack of willingness" to let the father be a meaningful parent.
"Certainly her actions in removing [the girl] from ... and hiding from him...mean that he has had no ability to be involved in her life," said Judge Coyle.
Psychology reports accepted by the overseas courts also ruled the father - not the mother - was the primary attachment figure.
But because of the length of their separation, the mother was now her primary attachment figure.
And she would stay in New Zealand if the Family Court ordered her daughter to return to her birth country.
Losing her mother and leaving her life in New Zealand would be "cataclysmic" for the girl, said Judge Coyle.
Despite the mother's actions in deliberately flouting a foreign court order and the father's involvement in their daughter's life, Judge Coyle found returning the girl to Europe was not in her best interests.
Doing so would put her in an "intolerable situation", in a psychological sense, which is part of the legal test.
However, Judge Coyle did not revoke a previous court order preventing the daughter from leaving New Zealand.
The judge also did not return her passport.
This leaves the door open for the father to seek day-to-day care of his daughter in New Zealand.
"There is a real risk that if I were to discharge that order, then [the mother] may attempt to flee."
However, the father has appealed the Family Court decision to the High Court.
Despite his anguish over the past few years, he wants to share custody in his country with his former partner.
She did not have to stay in New Zealand, he said, and offered to let her live in one of his rental properties.
"I don't have any bitterness. I just want to see my daughter."
