Generally speaking, if the custodial parent and the child are living in Kings County, the Kings County Family Court would have jurisdiction. A review of the court papers in the matter might reveal additional information, which could indicate a different answer would apply to your situation. You should consult with an attorney to discuss confidential details of the matter and have all the paperwork reviewed. Good luck!
Any party to an action may bring a motion to change venue based upon a showing of good cause. This can include a variety of factors, including the availability of material witnesses, etc. If the child is residing in the venue, that is persuasive, as the law guardian will have access to their client. Feel free to contact me at (516) 368-2484 to discuss your matter in greater detail.