"She shows us our room."
Translation:Ŝi montras al ni nian ĉambron.
Is the following actually incorrect? "Ŝi montras nian ĉambron al ni." I didn't think the arrangement of the what was being shown and to whom it was being shown would matter provided I used the preposition "al" to clarify.
The 'n' gets added to the end of nouns under certain circumstances, including when nouns are used as direct objects (such as "cxambron"). However, you generally don't add an 'n' to nouns when they're part of grammatical constructs such as prepositional phrases (the Esperanto phrase "al ni" translates to "to us"; the "to" is implicit in the English sentence due to "us" being expressed as an indirect object).
To add to this, the accusative is used in a prepositional phrase if you need to indicate movement (on vs. onto, in vs. Into, etc.). It's just not necessary with al because it already indicates movement.