The phrase «التي هو في بيتها» is not simply a household address. If bare identification were the aim, a different expression might suffice. The clause instead depicts a setting in which the moral test was especially intense.
First: the woman had access to Joseph within the household.
Second: he maintained integrity despite that proximity.
Result: attention is directed not only to the attempted seduction but also to his response in these particular circumstances.
This is a case of reinforcing the point of the discourse (تقرير الغرض) through information encoded in the relative clause.