When is mixing within the family unlawful (haram)?

The term "family" is an umbrella term; it may refer to relatives who are not mahram (unmarriageable kin), in which case mixing with them is anar evil and forbidden due to the corrupting influences that result from it. It may also refer to mahram relatives, in which case there is no harm in their mixing, because the Shar‘iah has permitted a man to be alone with his mahram woman. The proof for this is the hadith "The hamw [in-law] is death," which, a fortiori, indicates the permissibility of mixing among mahram relatives. This is a point of consensus among scholars, with the caveat regarding the limits of what may be seen of mahram relatives, and on condition that there is no fear of fitnah (temptation/strife).