Aside from "home" or "household", I understand that 家庭 can mean "family" as well. In such case, is there any difference in terms of usage or nuance between 家庭 and 家族? when is it more suitable to use 家庭 instead of 家族?
Regardless of how they may be rendered in the natural English, 家族 always points to people, while 家庭 always place. In other words, 家族 is a group united by kinship or whatever that often lives together, or its member; 家庭 is an environment that enables those people to gather and spend a private life (as opposed to "workplace" etc.)
Many words can be only used along with either of them, or change drastically on which they are used with.
家族訪問 family visit (as visa applicants do)
家庭訪問 home visit (as doctors do)
家族向け (a category of cars, movies, video games, tour packages...)
家庭向け (a category of prepared foods, video game consoles, vacuum cleaners...)
○ 家族写真 family portrait
× 家庭写真 (a photo records someone's lifestyle?)
× 家族料理 (a family's symbolic meal?)
○ 家庭料理 homemade food