I am sorry for your loss. You need to discuss this scenario with your probate attorney and/or a local tax professional.
Considering that the property is in probate, there is almost certainly not a trust involved here (which would bypass probate).
Regardless, New York State law, to the extent of my knowledge of same, provides that title vests in the heirs (legatees or devisees) immediately upon death. Whether this would dictate reporting the rental income, expenses, et al, on a 1041 or individual income tax returns should be discussed with your attorney or tax professional (although I suspect the second half of the year could be reported on a 1041 with the children as beneficiaries).
