I'd act badly with love to get a life of luxury (5,4)

I believe the answer is:

dolce vita

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'get a life of luxury' is the definition.
I can't judge whether this definition defines the answer.

'i'd act badly with love' is the wordplay.
'badly with' indicates an anagram (letters in the wrong order).
'id'+'act'='idact'
'idact' with its letters mixed up with 'love' can make 'DOLCE VITA'.

'to' acts as a link.

Can you help me to learn more?

(Other definitions for dolce vita that I've seen before include "Life of luxury (Italian)" , "Hedonistic existence" , "good times" .)

I've seen this clue in The Independent.

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