Chuck and Di's time with children (5)
I believe the answer is:
ditch
'chuck' is the definition.
(both can mean to abandon or throw away)
'di's time with children' is the wordplay.
'time' becomes 't' (abbreviation).
'with' is a charade indicator (letters next to each other).
'children' becomes 'ch' (genealogical abbreviation).
'di'+'t'+'ch'='DITCH'
'and' is the link.
(Other definitions for ditch that I've seen before include "Land in water" , "drainage feature" , "Drop" , "Drainage channel" , "side of field?" .)