Children captured by that mean, horrible enforcer (7,3)
I believe the answer is:
hatchet man
'enforcer' is the definition.
(someone who does unpleasant work for someone else)
'children captured by that mean horrible' is the wordplay.
'children' becomes 'ch' (genealogical abbreviation).
'captured by' means one lot of letters goes inside another.
'horrible' indicates anagramming the letters.
'that'+'mean'='thatmean'
'thatmean' with letters rearranged gives 'hatetman'.
'ch' placed into 'hatetman' is 'HATCHET MAN'.
(Other definitions for hatchet man that I've seen before include "intemperate critic" , "malicious critic" .)