House constructed badly in Virginia (5)
I believe the answer is:
villa
'house' is the definition.
(I know that villa is a type of house)
'badly in virginia' is the wordplay.
'badly' becomes 'i'll' ('ill' can be adverbial as in 'ill-advised').
'in' is an insertion indicator.
'virginia' becomes 'va' (US state abbreviation).
'ill' put within 'va' is 'VILLA'.
'constructed' acts as a link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for villa that I've seen before include "Large country house" , "Country house in Italy or France" , "Roman domicile" , "Roman or suburban house" , "Country residence" .)