How does Euripides explore the complexities of family in Medea?

Family life in Medea is presented as a source of conflict and chronic instability. Medea defies her father and, by extension, the established social norms by helping Jason to escape Colchis with the Golden Fleece. Though she abandons her family, Medea wants to start another one with Jason. She seeks the kind of stability that only an ordered family life could give to a woman in ancient Greece. At that time, women were defined almost exclusively by the role they played within their families as wives, daughters, and mothers. In helping Jason make his escape, Medea is hoping to exchange one conventional family structure for another. She knows how crucial it is for her to have a role in life. That is why she makes Jason promise her that he will marry her.
This is also why Medea's reaction to her abandonment by Jason is so bitter and vengeful. Jason's desertion has left her without any kind of family structure or support network. In ancient Greece, she is almost a nonperson, a woman without any kind of meaningful status in society. As Medea effectively has no place to go and nowhere to turn, she rejects the society that has rejected her and systematically sets about undermining its values, especially its valorization of the traditional family unit.