Dogs responsible for mother's quarrels (8)
I believe the answer is:
mastiffs
'dogs' is the definition.
(mastiff is a kind of dog)
'mother's quarrels' is the wordplay.
'mother's' becomes 'mas' (ma is a kind of mother).
'quarrels' becomes 'tiffs' (tiff is a kind of quarrel).
'mas'+'tiffs'='MASTIFFS'
'responsible for' is the link.
(Other definitions for mastiffs that I've seen before include "man's best friends?" , "Powerful deep-chested dogs" .)