My sympathies for your family's loss. The executor must file the will with the surrogate court in the county where the decedent last resided. This is public record and can be accessed through the court clerk. According to the following code, heirs (and that includes heirs at law- ie blood relatives not named in the will) must be notified of the proceeding prior to the issuance of Letters (these Letters give the executor court permission to manage the estate).
Here is a copy of the relevant code:
Before letters are issued there shall be filed in the court a notice entitled in the proceeding stating the name of the testator, the name and address of the proponent, and that the will of the testator has been offered for probate or probated, as the case may be. The notice shall further set forth the name and post-office address of each person named or referred to in the petition who has not been served or has not appeared or waived service of process and shall state whether such person is named or referred to in the will as legatee, devisee, trustee, guardian or substitute or successor executor, trustee or guardian. The notice shall further set forth the name and post-office address of the attorney general of the state of New York if the will that has been offered for probate contains a charitable bequest which is either to an unnamed charitable organization or is in an unspecified amount, including but not limited to, a bequest of all or part of the residuary estate. (a) Where by the terms of the will an interest in a trust or other fund or property has been limited in any contingency to the persons who shall compose a certain class upon the happening of a future event it shall be sufficient to name only the persons in being at the death of the decedent who would constitute the class if such event had happened immediately before the date of such notice, and who have not been served or appeared or waived service of process. (b) Where by the terms of the will an interest in a trust or other fund or property has been limited to a person who is named in such notice or who has been served or has appeared or waived notice of process, and has been further limited upon the happening of a future event to a class of persons described in terms of their relationship to such person it shall not be necessary to name such class of persons. 2. There shall be filed with the notice proof by affidavit of the mailing of a copy thereof to each of the persons required by the preceding subdivision to be named in such notice, and if any person is an infant or an incompetent, of the mailing of a copy thereof to the person or persons upon whom personal service of process is required to be made with respect to the infant or incompetent. When it appears by the petition for probate that the name or address of any person referred to in this section is unknown mailing to such person of the notice herein described shall not be required. 3. Upon the probate of an estate and distribution of its assets, if any, under this chapter, if an undistributed asset is subsequently found by the estate, the surrogate's court that granted such probate petition shall maintain jurisdiction and shall not require any additional service of the notice required by this section to be served again by the estate, unless such previously undiscovered asset has an estimated value of more than five thousand dollars or it has been more than seven years since the distribution of the assets pursuant to the original probate. (SCP 1409)
The parent or guardian of minors are to receive notice of proceedings affecting a minor's interest.
Here is a checklist of requirements the executor must comply with:
An executor can be removed, upon petition, if they breach their fiduciary duty to the estate; this includes notifying heirs of the process, so that any objections to the will/executor can be filed, and also so that the heir can remain informed as to the status of the estate.