Small bath delivered to large yard reluctantly (10)

I believe the answer is:

stubbornly

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'reluctantly' is the definition.
Both the answer and definition are adverbs. Maybe there's a link between them I don't understand?

'small bath delivered to large yard' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'bath' becomes 'tub' (synonyms).
'delivered' becomes 'born' (as in a baby being delivered).
'to large' becomes 'L' (eg in clothes sizes).
'yard' becomes 'y' (abbreviation).
's'+'tub'+'born'+'l'+'y'='STUBBORNLY'

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

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