The game guid states something along the lines that if one parent dies and there is a child or children old enough to take over the house there will be a clickable in the "Family" section that will let you choose who gets to take over the house.

Esther - I think there is a limit of 6 children on the family, as there are only six beds in the kids room. If the older ones come home for a visit where would they sleep if you didn't have a bed open for them?