avhaben: I believe you’re mistaken. I was told by many people, including Rabbonim, that all of R’ Moshe’s children had mixed seating at their weddings.
As for MO weddings, you have no clue what you’re talking about. There is a mechitzah between men and women, and there is no mixed dancing.
As for men seeing the women, I’m not sure about the halachos. Is there an issur of men seeing women dance, or only to dance together? In shuls, there is this recent idea that the women must be completely hidden from view, when this is NOT the halacha. They must just be separated.
I don’t know what the halacha is regarding dancing. I looked in the Shulchan Aruch, and I didn’t see anything about watching a woman dance. Does anyone have a source where it’s brought down?