Would you please correct me in choosing the words and arranging them?
Taking into account the people's state of the household , we should conduct research during which or through which faithfulness to the individual people in exchange for one another will be detected.
By the phrase "the people's state of the household", I mean: the situation, circumstance, or mood which household or each of the members of household have.
By "conduct research", I mean: we are going to do research.
What kind of research? The research through which we will find how faithful the people are to one another.