She posted on Facebook that Pearce was "very close" to Puna's family who had allowed their daughter to travel with him. He had previously taken her other siblings on trips overseas.
"He is very close to the family that owns the land he leases. He's become a second grandfather to this family's children," she wrote.
"He comes to the USA at least once a year. As these children have gotten older he's been bringing them for vacations in the US. Basically showing them there is a huge world beyond their little island."
Miller said Pearce had all the correct documentation including "permission from her parents, her passport, notarised documents, everything CBP could need to pass them through Customs".
"CBP still took Puna away from Marc. CBP contacted the child's parents in the Cook Islands, the parents tell CBP that Puna was allowed to be travelling with Marc. CBP still doesn't return Puna.
"Marc has not seen Puna in three days. He cannot find out where she is being held, or by whom. They will not tell Marc when she will be sent back to the Cook Islands."
Miller said Puna has never travelled overseas or left the Cook Islands before.
"She has never been to a big city. She is now alone in a strange place, with strange people, and they won't even let the one person in the entire country who she knows see or talk to her."
Her mother Ngatuaine Raela told the Cook Island News with the incident now gaining worldwide attention she now just wanted her daughter home - "te inangaro ua nei au I taku tamaine kia akaoki ia mai."
Sometimes he took the kids to school and picked them up, provided cakes for their birthdays and was good to the whole family, she told the Cook Island News.
She confirmed that Pearce has phoned twice from the US to inform them about their daughter and insists that he does not know where the US authorities are holding her.
Secretary of the Ministry of Foreign Affairs and Immigration (MFAI) Tepaeru Herrmann told the newspaper they were aware a Cook Islands national was currently in the care of United States (US) authorities.
"MFAI has prioritised attention to this matter and is continuing to work closely with domestic and international agencies including the New Zealand Ministry of Foreign Affairs and Trade who are providing consular assistance to the Cook Islands national in California."
The ministry was giving "priority attention" to the matter, that involved a number of complexities which require multi-agency, transnational co-operation.
An MFAT spokesperson told the Herald they were currently "working with the Cook Islands Government to facilitate the return of a child, currently in the care of the US authorities, to the Cook Islands".
"For privacy reasons, no further information will be provided."
