Father, at home, is a nuisance (4)
I believe the answer is:
pain
'a nuisance' is the definition.
('pain' can be a synonym of 'nuisance')
'father at home' is the wordplay.
'father' becomes 'pa' (pa can mean dad or father).
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'pa'+'in'='PAIN'
'is' acts as a link.
(Other definitions for pain that I've seen before include "Annoying person" , "Hurt feeling" , "Mental distress" , "Unpleasant sensation" , "nuisance to be put up with" .)