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You have to go to Family Court and file for custody and a temporary restraining order
to bring her back here.
The Court decides on custody based on the rule of thumb of "best interest of the child
." This includes, but is not limited to, general stability of the parent, financial stability, indoctrination of the child in the current school and environment, household condition and living condition of the child, other persons living in the house, etc.
The courts generally do not like to split the custody 50/50 since this is hard on the child – imagine having to move every half a year.
One parent usually becomes the main caretaker (in many states this is called the managing custodian) and the other parent becomes the "weekend" parent (often called the posessory custodian) which is every Thursday, every other weekend, and alternating holidays. The minute points of the custody can either be decided by the parties or the Court, if the parties cannot come to an agreement.
Even if a parent does not get managing custody, they are almost guaranteed the posessory custody unless they have a drug problem, alcohol dependency, or an unsafe home environment. Abuse and or neglect of the child or previous children are an almost automatic bar for even posessory custody, although supervised visitation
may be granted by the Court.
After you file, the Court will issue a TRO. Get a certified copy of the TRO, go to either the Greek consulate or some refutable translation company, and get the order translated into Greek. Once you do, either have the consulate send that TRO to the police of the city where she is or do it yourself. The police will go to her and investigate and MIGHT make her cooperate, but there is no telling. Sorry, but outside the US, cooperation with US laws is voluntary for other UN states, even if it's on treaty... But even if she doesn't do this, you can file a Motion for Contempt and if she ever comes back to the US, you can have her arrested and brought into court. Knowing this, she might cooperate.
Best of luck in your matter! I'm here if you need any more clarification or follow up info.
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