They have to be filed for probate. You can get an order for production of the will under
New York Surrogate's Court Procedure Act § 1401.
Proceeding to compel production of will -
Whenever it shall appear to the court, sua sponte, or by the petition of a person authorized under the succeeding section of this act to present a petition for the probate of a will, that there is reasonable ground to believe that any person has knowledge of the whereabouts or destruction of a will of a decedent the court may make an order requiring the person or persons named therein to attend and be examined in the premises. Service of the order must be made by delivery of a certified copy thereof to the person or persons named therein either personally or in such manner as the court shall direct. The court may either in the order or otherwise in the proceeding require the production and filing in court of any will of the decedent which it finds is in the possession or under the control of the respondent. The court may impose the reasonable attorneys fees of the petitioner in such a proceeding against a respondent when the court determines the respondent did not have good cause to withhold production of such will or codicil.
The Executor named in a will has no legal authority to act as executor until appointed by the Court.
The provisions of the wills are generally enforced and it does not matter if one child acted as a caregiver - that is not a factor in interpreting a Will.
You can get a free consultation from some of the NY probate attorneys listed by location here.
Please follow up on this with a local attorney.
I hope this information is helpful.