Who has a right to be present at an accounting of an estate?

First off I am so sorry for your loss.  Now, the formal and informal procedures that surround estate probate and an accounting are best asked to an attorney in your state.  I am assuming here that you do not have an attorney, which may be an issue for you as the executor.  You obviously need someone to watch your back here.  It is unclear that you have to formally convene for the accounting of the estate.  What is clear here is that your brother-in--law is objecting but seems to have no standing to do so (he did not inherit).  At this point in time I think it may be best for you to have the proceeding formally in court.  Here is the protocol for New Jersey:

The Executor/Administrator may be required to make a final accounting to the Court.  Usually this accounting is informal and does not require a Court appearance.  An informal accounting must be approved by all interested parties (beneficiaries) and the Attorney General of the State of New Jersey (in the case of a charitable beneficiary).  If an interested party wants to challenge the  accounting, then a formal Court hearing would be necessary.

 I think you should request that the court issue you a hearing date.  The Judge will keep everyone in line and expel your brother in law if he gets out of hand.  Protect yourself.  Good luck.