How have its cultural and historical contexts influenced your family’s priorities, the organization of family life, and the division of family roles? How can I exercise my sociological imagination by placing my family experience in its larger sociohistorical context?

The division of family roles is a sociological, historical, and cultural phenomenon. Family roles and gender roles differ from culture to culture, nation to nation, and even in different cultures in the same neighborhoods!
For example, in western culture in the United States, there is a history of middle-class women not working outside the home and instead raising their children. Today, even though many middle-and-upper class women work, it is still assumed that mothers take the primary caregiving role towards their children—that is why companies offer "maternity leave" but hardly ever offer the same leave for fathers. In contrast, in Finland, paternity leave is offered and fathers spend more time with their children than their mothers.
Every family will have its own answer to this question as the sociological issues and historical events that have meaning to each person and family is based on position in society—things like race, class, and gender. As a queer person, my family is shaped by historical and sociological contexts: My partner and I are not married because I did not grow up imagining getting married, as gay people were not legally allowed to get married when I was a child. Even though this has changed in recent years, my own imagination of my life is shaped by this history. I am working-class and a similar gender to my partner, so we divide our household labor (dishes, laundry, cleaning) equally instead of dividing it by gender or the amount of time we have at home. These are a few examples of the way that history influences the priorities and organization of my family.
One way to question the organization and priorities in your family is to think about different parts of home life and interrogate them individually. For instance: who is in charge of your household chores? Why? Are there historical events that precipitated this (for instance, the expectations of a stay-at-home mother that was culturally popular in the 50s?) Who does the cooking? Why? Are there sociological factors that influence this? (For instance, in my Jewish culture, women often hold onto the family recipes and pass them down matrilineally).
https://www.theguardian.com/lifeandstyle/2017/dec/04/finland-only-country-world-dad-more-time-kids-moms