In order to honor the court order and allow your ex to claim the child, you would give your ex a signed form 8332. In Turbotax, you would indicate that the child lived with you, and that you are releasing the dependent to the other parent with a signed form 8332. Turbotax will still allow you to qualify for EIC and head of household, if you otherwise qualify. If you are then blocked from e-filing, it can only be because your ex claimed the child as if the child lived with him, which is not correct and which would allow the ex to claim excess tax benefits. You would mail your return, mail the form 8332 to your ex, and suggest your ex re-check their return to make sure they filed correctly.
If you do not want to honor the court order, that is up to you. Your ex would have to file a complaint with the NJ court, and if the ex is himself in violation of parts of the order, that might influence the judge's decision. But it;'s up to you.
