Manage to convince, perhaps cuddling wife (4)
I believe the answer is:
sway
'manage to convince' is the definition.
(to sway someone is to influence or convince them)
'perhaps cuddling wife' is the wordplay.
'perhaps' becomes 'say' (both can mean 'for example').
'cuddling' is an insertion indicator.
'wife' becomes 'w'.
'say' enclosing 'w' is 'SWAY'.
(Other definitions for sway that I've seen before include "Rule; move to and fro" , "Influence; dominance" , "Totter; influence" , "Bend; influence" , "Influence; rule" .)