I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
Lawyers do not make custody decisions, judges do. When there's a dispute, only the judge's decision bears weight in the absence of an agreement. But lawyers generally have an ethical obligation to do what is in their client's best interests, which gives them a lot of room to negotiate a child custody dispute before getting into a courtroom.
You have the ability to file a Motion for Modification asking the judge to change the order so you have custody, not supervised visits. You can use any facts that show it's in your son's best interests to live with you. You can also present evidence of their plans to move out of state and show the original order that prohibits him from going. The girlfriend has NO LEGAL AUTHORITY WHATSOEVER, as she is not a parent. She can't legally decline your supervised visits. If your ex is allowing her to do so, then he's in contempt of court. A motion for contempt can be filed at the same time as a motion for modification.
Before you do anything else, read the original court order. See if there's a clause near the end that says, if you have to bring a motion for enforcement, he has to pay for your attorney's fees. It's sometimes in there, and if that's the case, you can hire a lawyer who will go after your ex to get payment.
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