Custody battle ended shortly after flu got out of control (3-2-4)
I believe the answer is:
tug-of-love
'custody battle' is the definition.
'ended shortly after flu got out of control' is the wordplay.
'ended' becomes 'over' ('over' can be a synonym of 'ended').
'shortly' means to remove the last letter.
'after' says to put letters next to each other.
'out of control' indicates anagramming the letters.
'over' with its last letter taken off is 'ove'.
'flu'+'got'='flugot'
'flugot' anagrammed gives 'tugofl'.
'ove' after 'tugofl' is 'TUG-OF-LOVE'.
(Other definitions for tug-of-love that I've seen before include "Conflict over the custody of a child" , "Phrase for dispute over custody of a child" .)