Parents taking in large island's capital (5)

I believe the answer is:

palma

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'island's capital' is the definition.
'palma' can be an answer for 'capital' (I've seen this before). I'm unsure of the 'island's' bit.

'parents taking in large' is the wordplay.
'parents' becomes 'pama' (Pa and Ma).
'taking in' is an insertion indicator.
'large' becomes 'L' (eg in clothes sizes).
'pama' enclosing 'l' is 'PALMA'.

Can you help me to learn more?

(Other definitions for palma that I've seen before include "Balearic port" , "Capital of the Balearic Islands" , "Spanish town" , "tourist centre in the Med" , "Capital of Majorca" .)

I've seen this clue in The Guardian.

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