Animosity from rotten family (3,5)
I believe the answer is:
bad blood
'animosity' is the definition.
(synonyms)
'rotten family' is the wordplay.
'rotten' becomes 'bad' (similar in meaning).
'family' becomes 'blood' (I've seen this in another clue).
'bad'+'blood'='BAD BLOOD'
'from' acts as a link.
(Other definitions for bad blood that I've seen before include "Hatred - ill-feeling" , "Feeling of animosity or hostility" , "Ill feeling of tainted sanguinary sort" , "Rancour" , "Hostility or ill-feeling, from tainted gore" .)