Dear do I have any rights in this case?
Perhaps I might provide an answer to your question.
At a minimum, you have the right to not be illegally evicted. Any time any one threatens to "evict" that means evict by use of a court proceeding. New York does not allow self-help or do it your self eviction. Your husband's probation officer might be interested if your ex threatened you and the children with an "illegal eviction."
Do you have any rights in the house? Are you an owner? Did your divorce decree provide for support for you and for the children by your husband? Does he owe you any child support or alimony? If so, inform your family law attorney right away that your ex threatened you with eviction and owes child support and alimony.
If you have an ownership interest in the house your ex cannot use the civil court to "evict" you and the children because you are a co-owner.
If you have no ownership interest in the house but your ex owes money for you and the children your attorney may try to resolve this by having your ex quit claim the deed to you.
You need an attorney to protect you and the children.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.