a family may include parent and their children, grandparents, aunts, uncles and cousins, as well as more distant relatives. But when British and American people use the world family they often mean only a mother, father and their children, in a general social context 'the family' is usually taken to mean this nuclear family.
the family unit
Society in Britain and the US is traditionally based on nuclear family living in the same house and closely involved in each other's lives. Fifty year ago, the typical family was a husband and wife, and two or three children, T eh father spent all day at walk and made most of the decisions about hoe the money he earned was spent. the mother stayed at home to manager the house and look after the children. Children were expected to obey their parents.