Not so. In many states, the statute states that its in the best interest of the children to be able get custody back or not, its not important that you are the mother or not. If she gave up custody, she will have a difficult time getting it back.
In New York, as with most other states, the Court will need some real significant reason to modify an existing custodial arrangement. If the mother of the child voluntarily conceded custody to the father, she would have to demonstrate to the Court that some significant change of circumstances has occurred since then, and that it would be in the best interests of the child to alter the custodial arrangement. This is typically a very high burden to meet.
Mr. Rosen practices matrimonial and family law in Great, Neck, NY. His response here is not legal advice and does not create an attorney/client relationship. The response is in the form of legal education and is intended to provide general information about the matter in question. Many times the questioner may leave out details which would make the reply unsuitable. You are strongly advised to confer with an attorney in your own state to acquire more information suited to your particular circumstances.