Was the husband wrong to house his wife with his family? Is the wife considered disobedient for leaving with her mother without his permission? Is the wife’s father considered to have broken his promise, and how should he be dealt with in the future? Should the wife apologize to the husband’s parents for her actions?

It is the wife's right to have independent accommodation, and she is not obliged to live with the husband's family. She has the right to refuse to do so. The reasons mentioned by the wife justify her refusal, and she is not considered disobedient (nashiz). She is not required to apologize to your family. However, her apology to your family might mend the relationship.