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The answer is somewhat complicated but generally 'yes', the other parent can return to the US and seek review. But this review has to be based on factors pertaining to how the children are being treated or fitness (or unfitness) of the other parent. Simply not liking the past judgment is not enough to overturn, there has to be a genuine basis to amend which would have nothing to do with the past perceived unfairness of the order. For example if the father is being a 'good' parent and the children's needs are being met, the courts are far less likely to amend, but if the father is unfit, abusive, neglectful, and so forth, then there may be grounds under which the local courts could issue their own ruling.
I appreciate your follow-up. As far as your additional facts, I figured that this would be the case. But my answer would still not really change--you need to show evidence that the other parent is not acting in a 'fit' manner. But again, claiming that you were unfairly treated in a foreign court is not enough so long as state laws were not violated.
No, the parent would not. That parent would still have to prove and show to a US court that the other parent is unfit. Even with a claim for favortism and legitimate bias, if the parent picked by the courts ends up being fit and competent, and the child(ren)'s needs are being met, the court won't change custody.