Hi! :)
This quest is a bit bugged, the shed is upstair, between the mayor's room and the sister room.
If you need to meet the mayor's wife in the shed, here's what you need to do : talk to the maid < go upstair without going out.
If you go out the wife will disappear, you can make her pop again by talking to the maid! So : don't go outside! ;)