So, this is a case of "de facto" termination of parental rights, and the "child's best interest" standard simply is insufficient to protect either the child's or the father's interest. Further, since the move is likely to be a de facto termination of parental rights, previous cases have indicated (if I recall correctly) that a much stricter standard must be applied before deciding the move is in the child's best interest.
Thus, I believe there is an appealable issue. Neither the trial court nor the appellate court applied the proper standard for an international move which is effectively a de facto termination of parental rights. If the trial and appellate courts used the CBI standard, that is a clear error, I would believe, and should be reversed and remanded to apply the proper standard; i.e., much stricter scrutiny.
On the other hand, if the proposed relocation were to a country that was a signatory to the Hague Convention, then I would probably believe the Appellate Court would not be reversed (even though I personally disagree with the decision).
That's my guess.
Good Luck.