Family dispute over death benefits

My father passed away last nov 25,2016 and he worked in cidg. We know that we will get large amount of money as death benefits but the problem is my mother. My mother left us and chose to stay with another man 9 years ago and she has one daughter with that man but he also died last 2010 and instead of going home to us,my mother chose to find another man. My father is the one who stood as mother and father to us. It also came to a point that my mother left to us our half-sister while she had yet another man and my father was ok with it. Now as we are doing the processing of my father's death benefits,we found out that he did a certificate of beneficiary with me and my brothers as dependents but not my mother. She is not listed and one agency told us that she will not be honored as beneficiary. The question is, will my mother be entitled to any of his benefits? The truth is we,her children, does not want her to get any of it because of what she had many years ago.
Hope you can answer my question.