Reconstituted family
A reconstituted family (also known as a blended family) is the sociological term for the joining of two adults via marriage, cohabitation or civil partnership, who have had previous relationships and children from them.
A man breaks up with his wife and got divorce and either re-married another woman or moves in with her. He also brings his children from his previous marriage. Therefore, it becomes a reconstituted family. The children will be known as step children.