How can my sisters and I take control of the estate and is there any ramifications regarding my mother's medical care?

My brother passed away suddenly and did not leave a will. He was not married and has no children. It is left to me to settle his estate. From what I am reading online, it appears that, if there is no spouse or children, then next in line to inherit are the parents. Therein lays the problem. Our mother has Alzheimer’s and it is advanced to the point where she barely recognizes us. My father is already deceased. I think, if I am reading things correctly, my mother is the beneficiary even though she is incapacitated. I know that my brother would have wanted to divide his estate among his 3 siblings and our mother but he never put that in writing. Will anything happen to her coverage when the inheritance is around $400,000?