First, you conveniently ignore Cantate Domino.  You might acquire Denzimger's Enchiridion Symbolorum in which you will find a list of ex cathedra decrees.
Secondly, the Book of Exodus provides general instructions for the requirements of the paschal feast.  You don't take into account the traditions of those same Hebrews who separated men and women (with their children) during any religious ceremony.  Orthodox Jews still practice this way, even in the synagogue, separating men and women with a mechitzah, a curtain or divider of some kind.  This practice also occurs at weddings and bar mitzvahs.
Interviewed by the Jewish Journal, Rabbi Perry Netter of Temple Beth Am and Rabbi Dan Moskovitz of Temple Judea explain why they are accommodating a "man-only" Seder meal.  Part of their interview reads:
"That’s why, he said, men were traditionally separated from women, because it was distracting to men."
Whether or not you agree with the practice matters not.  Understand that it was the custom.