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The man complained that the children, who are aged 10 and eight, had been taken without his agreement, and a High Court judge has ordered their return to Ireland.
Mr Justice Mostyn was told that the children had been living in Bradford, West Yorkshire, with their mother.
He heard that they had been born in Ireland and concluded that Irish judges should make decisions about their welfare.
The judge has outlined detail of the case in a written ruling published on Tuesday after considering arguments at a recent private hearing in the Family Division of the High Court.
He said the children could not be identified in media reports of the case.
The children’s mother accepted that they were, legally, “wrongfully removed from Ireland to England” during the summer of 2022.
But she said their father was aware of her plans to “relocate to England” and argued that they would be at a “grave risk of harm” if returned to Ireland.
She told Mr Justice Mostyn that she “cannot return to Ireland” and said she would remain in England if the children were returned.
The woman said she had “relinquished” her housing in Ireland and claimed that she would have “no means of supporting herself or the children”.
Mr Justice Mostyn said the “likelihood of an intolerable peril to the children” arose principally because the woman said she would not accompany them to Ireland.
“The court is always extremely hostile to having a gun held to its head,” he said.
“All of the supposed grave risk of intolerable peril is a result of the mother’s unlawful and wrongful conduct.
“It would be a remarkable example of the triumph of injustice over justice, of wrong over right, if a mother could clandestinely relinquish her housing, pluck the children out of school, remove them to England in breach of a court order and then state that she will not accompany if they are returned, thereby enabling her to present them to this court as prospectively abandoned, homeless, unschooled and destitute with the result that a return order is refused on that basis.”
Mr Justice Mostyn heard that the children’s parents had separated more than a year ago.
He heard that the man had, nearly three years ago, been granted a protection order in an Irish court after alleging that the woman had “assaulted him and thrown him out of the family home”.