i think I'm missing something here, I totally don't get the punch line.

I could barely even follow it. The dialogue seemed all over the place.

Seems like Yukiho is taking off her ribbons and Haruka is putting on a wig so that they can make AmiMami do the same challenge? (Guessing who is which from behind.)

Yep, lost me.

I think what is going on is that Mami and Yukiho had some "special time" together which is why Yukiho could tell if the twins undressed. As for the ending, Ami is ignoring Haruka and just talking to her ribbons while Mami is telling Yukiho to be careful of what she says because Yukiho nearly blew their cover. Or something like that.