Question: > 
> They inflicted gunboat diplomacy on these poor island people.
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> 
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Inflict means "to cause something harmful against", so this doesn't seem the right word.

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> They forced gunboat diplomacy on these poor island people.
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> 

This doesn't seem to be correct. A more neutral way to say this would be:

> 
> They practiced gunboat diplomacy on these poor island people.
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What's the correct verb to use here? I am not sure forced x on them is the most appropriate.

Answer: 
I would put a comma between "money" and "out":

"What's a lot of money, out of curiosity?"

It's fairly common usage in British English.
It's a little bit odd, though the meaning is clear enough.

More likely someone would say "Just out of curiosity how much is 'a lot of money'?", possibly shortened to "Just out of curiosity, how much is 'a lot'?" or even just "How much is 'a lot'?"