Did all the townsfolk know that Yuki is a wolf?
Probably no.

Nothing in the movie tells us that the people knew but decided to say nothing. If this was the case, I think there would be more details in the movie telling it.

Furthermore, if you imagine normal people, thinking that someone can transform into a wolf is not the first idea you will get. So even if you see a dog with some cloth just after seeing a little girl with similar clothes, you are not going to think "hey, the girl transformed into a dog/wolf !" or if you think/say it, it's only to make a joke, because you cannot imagine it to be true.

The goal of this scene is to give the spectator this feeling of "it was so close, the townsfolk nearly discovered the truth" which makes it a funny scene. Also, it explains that being the mother of such children is no easy, because there are probably many times when someone was nearly about to discover the truth.