Does this sound natural?
You just want to stay as rational as possible while you are in a different country.
No matter whose fault it is, just don't make trouble with locals.
But if you want to go down the road of trying to save your face, trying to get the advantage while you are having a dispute with them, things can and will go south.

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Two corrections:
You want to be as rational as possible...
save face

Suggestion: I would post something like this in notebook instead of questions so that we can give you better corrections. :)

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“Trying to win in every dispute” would be better than “ Trying to get the advantage when you were having a dispute with them“