Troublesome child is left with Gardner in Danube city (10)

I believe the answer is:

bratislava

I'm a little stuck... Click here to teach me more about this clue!

'danube city' is the definition.
'bratislava' can be an answer for 'city' (I've seen this before). I'm not certain of the 'danube' bit.

'troublesome child is left with gardner' is the wordplay.
'troublesome child' becomes 'brat' (I've seen this before).
'left' becomes 'L' (common abbreviation).
'with' is a charade indicator (letters next to each other).
'gardner' becomes 'ava' (actress Ava Gardner).
'brat'+'is'+'l'+'ava'='BRATISLAVA'

'in' is the link.

Can you help me to learn more?

(Other definitions for bratislava that I've seen before include "Capital of Slovakia" , "City" , "Slovakian capital" , "Capital of the Slovak Republic" .)

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

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