Black Hat = Good Father?

So my daughter (2 years old) is going to be "Imma shel Shabbat" at Gan. Basically every week a girl and boy pretend they are the parents in the kindergarten, and light shabbos candles, hand out grape juice etc etc. All of this is really sweet, but what bothers me is that they dress the kids up as Haredim. The father gets to wear a nice big black hat, and a "suit" and the mother wears a big head-covering. This is a Dati-Leumi Gan. I'm worried my lil girl is learning that good fathers must wear black hats!