Vacillate, having wife to maintain (5)
I believe the answer is:
waver
'vacillate' is the definition.
(I know that vacillate can be written as waver)
'wife to maintain' is the wordplay.
'wife' becomes 'w' (abbreviation).
'to maintain' becomes 'aver' (averring is a kind of maintaining).
'w'+'aver'='WAVER'
'having' is the link.
(Other definitions for waver that I've seen before include "Falter, be irresolute" , "Hesitate" , "Not be sure of" , "Show hesitation, begin to give way" , "Begin to weaken" .)