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Parent with ace coats providing raised hoods (5)

Ross

I believe the answer is:

mafia

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'parent with ace coats providing raised hoods' is the definition.
I can't tell whether this definition defines the answer.

'parent with ace coats providing raised' is the wordplay.
'parent' becomes 'ma' (ma can mean mum or mother).
'with ace' becomes 'a' (abbreviation. I am not sure about the 'with' bit.).
'coats' is an insertion indicator.
'providing' becomes 'if' (eg 'providing it's sunny' means 'if it's sunny').
'raised' is a reversal indicator (going up in a down clue).
'if' in reverse letter order is 'fi'.
'ma'+'a'='maa'
'maa' placed around 'fi' is 'MAFIA'.

Can you help me to learn more?

(Other definitions for mafia that I've seen before include "Gangsters" , "Italian criminal organisation" , "Criminal organisation with origin in Sicily" , "International crime organisation originating in Sicily" , "The Sicily mob" .)

I've seen this clue in The Times.
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