The Vilna Gaon writes in his allegorical commentary that the “house of women” represents this world, while the “house of the king” represents the World to Come.
Rav Chadidah says that in the gentile world, women are defined by the man’s house in which they dwell. A person’s rank, reputation, and nationality is paternal. In Judaism, however, very much depends on the mother. Earlier in the Torah, all of the matriarchs had their own individual tents, as in Rachel’s tent instead of the women’s tent (cf. Bireishis 31:33). True, one’s tribe and customs are paternal. But one’s very Jewish identity comes from the “women’s house.”