Yank's daughter with kid (4)
I believe the answer is:
drag
'yank's' is the definition.
(I've seen this before)
'daughter with kid' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'with' says to put letters next to each other.
'kid' becomes 'rag' (I've seen this in other clues).
'd'+'rag'='DRAG'
(Other definitions for drag that I've seen before include "car" , "gay party" , "such a nuisance" , "pain" , "Pull along with effort" .)