There was this japanese girl that married a westerner who was an aristocrat ( I don't know if it was one of those 'fake' marriages) . I remember that they went to a ball and everyone thought she was really pretty. Although at first she was shunned for being japanese.
I think her tutor was fell inlove with her. ( I don't know if I'm confusing this part with another manga).
The manga made an allusion to a japanese princess who also married a westerner.

I'm not sure if this is what you're looking for. The marriage is at the end, and there are no real love rivals, no tutor falling in love but the protagonist is a university student writing her thesis on this princess that married a westerner. She approaches the princess' grandson, who is an exchange student, in order to get info for her thesis. And at one point he does take her to a ball/party, and she's so pretty that no one recognizes her as her normal self.

Private Prince
http://www.mangaupdates.com/series.html?id=2596

Quite possibly, The Prince's Cactus? I don't know about a tutor, but the rest sounds like it.

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"How do you always find an excuse to get spontaneously naked!!"

- Absolute Boyfriend

I know it's not the prince's cactus, since I remembered that one quite well =D hehe.

but I know that there was a tutor and that tutor was the younger brother of the aristrocrat's friend.