The phrase "rather amused" is grammatically correct and can be used in written English.
It is usually used to describe a level of amusement that is more than just a little, but not quite strong enough to be described as "very amused." It adds a subtle emphasis to the level of amusement being expressed. Example: "I was rather amused by his silly joke." In this sentence, the speaker is indicating that they found the joke to be somewhat amusing, but not hysterically funny. The use of "rather" adds a touch of nuance to the level of amusement being expressed.
No use going back and am rather amused at being taken in by the Romany cousins.
And where was he? Escaping Enniscorthy, he's rather amused to find himself in Brooklyn.
At the same time, she's aware of -- and rather amused by -- another aspect of her character, a "cheerful French self" interested in the latest fashions and even, possibly, in romance.
In that connection I would have to say that I was rather amused to hear Lewis remark that it seemed a very long race indeed in Japan, which, as it ran for two hours, was just about right.
Fellini would have been extremely pleased and certainly rather amused to lean that Sophia Loren was playing his mother.
People were rather amused at how easy it was to disrupt the signal".
To be fair, both Tom and Ray played up the educated part of their backgrounds perfectly: they didn't discuss it with false humility like Brenda Patimkin in "Goodbye, Columbus," who tells Neil Klugman that she "goes to school in Boston," but rather with amused contempt.
Both Dewey and the other guy, Wade, have tried to kill Raylan in past seasons, but he mostly seems amused rather than angry.
When Leskov's own narrative voice appears in his stories, he observes human frailty with an amused rather than excoriating eye, as he does in "Deathless Golovan": "The house, to be sure, was a strictly pious one, where they prayed in the morning, oppressed and robbed people all day, and then prayed again in the evening".
Future political scientists will analyze (let us hope in amused retrospect, rather than in exile in New Zealand or Alberta) the precise elements of Poujadisme, Peronism and Huck Finn's Pap that compound in Trump's "ideology".
He wrote that political leaders who cry "tyranny" and "socialism" aren't trying to incite hysteria; rather, they're "so amused with their own verbal flourishes and the ensuing applause, that -- like the bloggers and TV hosts to which they cater -- they seem to lose their hold on the power of words".
