Shilly-shally over their runaway daughter (6)
I believe the answer is:
dither
'shilly-shally' is the definition.
(I've seen this before)
'over their runaway daughter' is the wordplay.
'over' says to put letters next to each other.
'runaway' is an anagram indicator.
'daughter' becomes 'd' (genealogical abbreviation).
'their' anagrammed gives 'ither'.
'ither' put after 'd' is 'DITHER'.
(Other definitions for dither that I've seen before include "perturbation" , "lather" , "State of high agitation" , "Stew" , "indecision" .)