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Cruelly, one French family duly stripped of uniform (8)

Ross

I believe the answer is:

unkindly

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'cruelly' is the definition.
Both the answer and definition are adverbs. Maybe they are linked in a way I don't understand?

'one french family duly stripped of uniform' is the wordplay.
'one french' becomes 'un' ('one' in French).
'family' becomes 'kin' (synonyms).
'stripped of' indicates named letters should be taken away.
'uniform' becomes 'U' (phonetic alphabet: alpha, bravo, charlie etc.).
'duly' with 'u' taken out is 'dly'.
'un'+'kin'+'dly'='UNKINDLY'

Can you help me to learn more?

(Other definitions for unkindly that I've seen before include "In an inconsiderate way" , "In an inconsiderate manner" , "In an unsympathetic way" , "Cruelly; inconsiderate" , "Unsympathetically, harshly" .)

I've seen this clue in the Sydney Morning Herald.
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