it's probably worth noting the exact misspelling is an added n, since we had some missing letters earlier. And yeah I'm not... sure we know where the Duchess' room is. That word makes me think it'd be the Queen of Hearts' throne room, but that's on the first floor. When we found her bedroom in the last event it was technically on the fifth but that doesn't line up with the clue about how many flights of stairs.

edit: I'm going to bed but my solid guess is second mansion, floor 3. I don't know if that's a specific room, but that's where my first guess would go to.