Who is entitled to a person's assets if they die without a Will?

When someone dies without a Will they die "intestate". Consequently the intestacy laws of the state where the deceased was domiciled as of the date of their death will control. Typically an estate is distributed to the surviving spouse, if any, and to the children of the deceased. Here, your grandfather predeceased your grandmother, so her estate would have been inherited by her children. Typically,in the case of intestacy, if a child predeceases their parent their share is split among the surviving children unless the deceased child left children of their own. So in this instance your mother's share would not go to your uncle since your mother left you and your sister. Accordingly you and she would inherit your mother's share.

Therefore your uncle appears to have overstepped his legal bounds. To be sure of your legal rights and remedies under specific state law you need to consult irectly with a probate attoreny  in the state where your grandmother died.