In one scene Anna was wearing his coronation dress inside of Oaken's store, but in the 次 scene she was wearing a different outfit. Where did she change clothes?

I meant her coronation dress, not his. Sorry about that mistake.

SHE CHANGE HER CLOTHS IN THE BATHROOM

Oaken has a changing room; think about it: he's running a sauna, so of course he'd have a place for people to go and change- and its a trading post too.