Persuaded prisoner to join man and daughter (9)
I believe the answer is:
convinced
'persuaded' is the definition.
(convincing is a kind of persuading)
'prisoner to join man and daughter' is the wordplay.
'prisoner' becomes 'con' (abbreviation for 'convict').
'to join' means one lot of letters go next to another.
'man' becomes 'vince' ().
'and' is a charade indicator (letters next to each other).
'daughter' becomes 'd' (genealogical abbreviation).
'con'+'vince'+'d'='CONVINCED'
(Other definitions for convinced that I've seen before include "Firmly persuaded" , "Quite sure" , "Totally certain about something" , "Absolutely certain" .)