Dad's backing Mum perhaps, that's obvious (8)
I believe the answer is:
apparent
'obvious' is the definition.
('apparent' can be similar in meaning to 'obvious')
'dad's backing mum perhaps' is the wordplay.
'dad' becomes 'pa' ('pa' can be a synonym of 'dad').
'backing' shows that the letters should be reversed in order.
'mum perhaps' becomes 'parent' (mum is a kind of parent).
'pa' backwards is 'ap'.
'ap'+'parent'='APPARENT'
'that's' is the link.
(Other definitions for apparent that I've seen before include "See 1" , "Obvious; seeming real" , "Noticeable" , "Visible - plain - presumable" , "Conspicuous" .)