The section 37 of the Indian succession act referred in your query is reproduced below:
Where intestate has left child or children only.—Where the intestate has left surviving him a child or children, but no more remote lineal descendant through a deceased child, the property shall belong to his surviving child, if there is only one, or shall be equally divided among all his surviving children.
By this the words "but no more remote lineal descendant through a deceased child" is the trump card to you. The widow of the deceased child shall not be a lineal descendent , hence in my opinion she may not be entitled to a share in her father-in-law's property.
You may decide to prefer an appeal quoting the same provisions of law and if possible with the support of some citations of settled laws in this regard.
You may proceed as intended.
