END of 'family'. The first PART conveys the idea 'of possession', 'belonging' as 'home' of 'the family'.The correct way of writing the same is 'The family's home' . APOSTROPHE (') is a punctuation USED for ' expressing belonging of a noun'.Note: Apostrophe (') is not to placed with pronouns. For INSTANCE: Nevada's doll. (usage of a name, noun.) Her doll. (usage of pronoun in the place of 'Nevada').Hence, option 1)