Based on your clarification, my bet was that the mother and father held the house as tenants by entirety (basically joint tenants for married folks). Then they partitioned it at the divorce, so that the two children and the mother would hold as tenants in common (without rights of survivorship), the mother holding 1/2, and the children holding 1/4 each. Therefore, the mother's 1/2 share goes through probate either through a will or through the law of intestacy (we would have to know more about who her relatives were to figure that one out).
But it's hard to be sure without seeing all the relevant papers. And blah, blah, talk to a lawyer.