Black ones containing family’s swimwear (6)
I believe the answer is:
bikini
'swimwear' is the definition.
(I've seen this before)
'black ones containing family's' is the wordplay.
'black' becomes 'b' (as in pencil classifications).
'ones' becomes 'ii' (I can't justify this - if you can you should give a lot more credence to this answer).
'containing' means one lot of letters goes inside another.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'ii' enclosing 'kin' is 'ikini'.
'b'+'ikini'='BIKINI'
(Other definitions for bikini that I've seen before include "Beach clothing" , "Skimpy bathing costume or Pacific atoll" , "Small two-piece bathing suit" , "Skimpy garment" , "Skimpy two-piece swim wear" .)