Well the 'other woman' is definitely not getting a 'widow's pension' or bereavement benefit from the state as she was not married to him.
Is your mother living with another man? If so, she is not entitled to claim. Does your mother fit the criteria here?
http://www.hmrc.gov.uk/manuals/senew/SE76171.h tm
If it is his private works' pension, he may have been entitled to name his partner as beneficiary, and not his wife.
Or she may be getting nothing, and your information is wrong.