Demanding son lives in temporary shelter outside (9)
I believe the answer is:
insistent
'demanding' is the definition.
(I've seen this before)
'son lives in temporary shelter outside' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'lives' becomes 'is' ('be' can be a synonym of 'live').
'temporary shelter' becomes 'tent' (I've seen this before).
'outside' is an insertion indicator.
'in'+'tent'='intent'
's'+'is'='sis'
'sis' placed into 'intent' is 'INSISTENT'.
(Other definitions for insistent that I've seen before include "Refusing to be thwarted" , "Emphatic" , "Constant" , "Determined" , "Not giving up" .)