Yes, you can file a custody petition in Family Court or Supreme Court to address this situation. In New York State, interstate moves without the consent of the noncustodial parent which will interfere with reasonable access to visitation and shared parenting are not allowed and raise serious issues for the court. The leading case on the topic is a Court of Appeals (state's highest court) case called Tropea v. Tropea which lists a number of factors which must be considered in allowing (or not) and interstate move by the custodial parent in a custody case. See, http://jackle.bo/_tropea .
This is a relatively "dicey" kind of case and you will need to move quickly before the move so the NY courts retain jurisdiction which they can possibly lose six months after a move (although arguably your case may be different because there is a NY decree or order). An attorney is helpful in this kind of difficult custody case; you can use the "Find a Lawyer" tab on this site or Google for "child custody" or "family law".
This answer is provided under the Avvo.com “Terms and Conditions of Use” (“ToU”), particularly ¶9 which states that any information provided is not intended as legal advice or to create an attorney-client relationship between you and me or any other attorney. Such information is intended for general informational purposes and should be used only as a starting point for addressing your legal issues. In particular, my answers and those of other attorneys on Avvo.com are not a substitute for an in-person or telephone consultation with an attorney licensed to practice in your jurisdiction about your specific legal issue. I can only answer your question based on the brief statement of facts you present in your question which may omit other relevant facts which would be disclosed in an in-person interview. While I attempt to provide reasonable care in answering your questions in an online forum which encourages attorneys to provide brief "off the cuff" responses within several hours of the posting of a question, I cannot perform any further detailed legal research concerning possibly relevant statutory or case law which might apply to your situation that I would normally do in the course of my representation of clients where an attorney-client relationship exists (and you are paying for my services!). You should therefore not rely solely upon legal information you obtain from this website or other resources which may be linked to an answer for informational purposes. You understand that questions and answers or other postings to the Site are not confidential and are not subject to attorney-client privilege. The full Avvo ToU are set forth at http://www.avvo.com/support/terms . In addition, while similar legal principles often apply in many states, I am only licensed to practice in the State of New York and Federal Courts. Any general information I provide about non-New York laws should be checked with an attorney licensed to practice in your State. Lastly, New York State Court rules (22 NYCRR Part 1200, Rule 7.1, available online at http://jackle.bo/_prof ) also require me to inform you that my answers and attorney profile posted on the Avvo.com site may be considered "attorney advertising" and that "prior results do not guarantee a similar outcome".
If you do not agree to the move, file a petition in Family Court seeking to prevent the move. It will be easier on everyone if you file before the move has taken place (consider moving the kids all over, or forcing them back to NY after a move as not the best for them either). Once the kids are out of the state for six months, New York will lose the ability to hear the case. Good luck.
Typically an agreement drafted by an attorney would ensure hat you have a set visitation schedule and would also have provided a radius clause or other mechanisms to address a potential move/relocation. You should consult an attorney about filing a petition/motion to address this move before your ex moves your children.
The content of this post is not legal advice and should not be relied upon as such. I am not your attorney and no attorney-client relationship has been formed based upon this exchange.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.