That depends heavily on how the family operates.

Historically speaking, the male head-of-household had dictatorial control over the ownership and expenditures within the household. Only in the last two generations have western women gained the right to hold down jobs and assume credit for large purchases, to own their own homes, and to take full custody of their children. The idea of emancipated minors, civil rights for children, and labor protections for young people are even newer. And there are plenty of reactionary political attitudes in the country that would see these reforms rolled back.

A family certainly can operate in a socialist capacity, when productive property and its surplus is shared equitably. But there are plenty of instances in which the head-of-house is functionally no different than a landlord, demanding the rest of the family live contribute surplus labor while existing in relative poverty.