My deceased grandmother owned her home and left no will. Are both kids entitled to 50% of the house?

My mother moved in with grandmother when my grandmother was diagnosed and died with terminal cancer in 2012. After her death my mom has continued to live in the house. He lives in Arizona and had no contact with her for years before she died. Recently we found out my uncle has been attemping to buy the house from the city but it's not for sale or behind on any taxes. My grandmother didn't have a will so wouldn't they both be entitled to the property? They each have paid the property taxes. My mom doesn't want to move or sell the property. What can we do?