Translates "her" as "sia"... should be " ŝia".
No it should not, unless she is dancing in some other female's room.
Why would it be sia if it were her own room?
Interesting, so we would still use sia if we were talking about a guy? "Li dancas en sia ĉambro."
Well, that could be the English translation as well. It is only context that makes us assume it is her own room. Anyway, I learnt something.
why isn't the accusative used here?
Accusative is not used, because there is nothing, which could demand its use. After prepositions like "en" or "apud" follows usually the nominative.
I had it right but then added the "n" !