However, the court said the children need not go back until the Christmas school holidays.
In the meantime, it is hoped an application by the mother in the German courts allowing her and the boys remain here will be “progressed as soon as possible”, the Appeal Court said.
The mother, a Polish national, and the father, a German, married in Poland in April 2010, and they subsequently lived in Germany.
The boys, the eldest now five and attending school in Ireland, and the other, three, were born in Germany.
The eldest boy underwent surgery for cancer in Germany in May 2014. The younger child was diagnosed with an epilepsy-related condition three months later.
The father was diagnosed with burn out syndrome and depression in 2013 and also suffered severe injuries in May 2014. The mother commenced counselling therapy in October 2014.
The Court of Appeal, rejecting the mother’s appeal against a High Court order the boys be returned to Germany, noted there was a dispute between the couple about an alleged affair the father had. This, the wife says, ultimately provoked her to leave her home in Germany and come to Ireland with the boys last December.
The mother’s sister and father, and other family members, live in Ireland.