Stubborn issue: mother's a nag and father's an ass (4)
I believe the answer is:
mule
'an ass' is the definition.
(thesaurus)
I don't understand the rest of the clue.
(Other definitions for mule that I've seen before include "Proverbially stubborn animal" , "Offspring of a donkey and a mare" , "Equine hybrid" , "Donkey-horse hybrid" , "Slipper - beast of burden" .)