Is a wife's service to her husband's family and performing household chores for their home, in addition to her own, obligatory upon her in Islam? And what is the ruling in Islam regarding a husband who compels his wife to serve his family?

Serving the husband's family is not an obligation upon the wife; rather, it falls under the category of good companionship. It is not permissible for the husband to compel his wife to serve his family. It is preferable for the wife to serve them if it does not cause her hardship, seeking her husband's contentment.