Is the wife obligated to obey and show dutifulness to her husband's parents? And if so, do they hold the same status as her own parents?

A wife is not obligated to obey her husband's parents or to serve them, nor is she required to honor them as she honors her own parents. However, she must treat them kindly, honor them, and avoid harming them. If she chooses to serve them, it is a good deed for which she will receive a great reward. Indeed, Fatimah, may Allah be pleased with her, used to serve and assist her husband's mother.