Is acting in anger and refraining from speaking with family, perhaps even disobeying them, considered correct because the mother socializes with men and the sisters went on a mixed university trip, and what is the way to deal with anashid in such situations?

One must honor and be dutiful to one's parents and treat them with kindness, even if they are disbelievers. It is not permissible to abandon them or treat them disobediently. Rather, one must advise them in the best possible manner. As for abandoning sisters due to their disobedience, it is permissible if there is hope for a beneficial outcome from it. If one breaks an oath regarding abandoning parents or sisters, an expiation for breaking an oath becomes obligatory.