The Kloyz building was probably inspirited by the Kloyz in Sadgora, the residence of Rabbi David Moshe's father, Rabbi Israel of Ruzhin, and his elder brother, R. Avraham Yaakov.
The Tsaddiks of Ruzhin-Sadgora dynasty did not pray with their Hassidim, but had a separate prayer room near the main prayer hall. This arrangement was started by R. Israel of Ruzhin and is noteworthy in all Kloyzn of his descendants (Asaf, pp. 372-3, Even, pp. 3, 83, 153).
Since the women did not take part in the Hassidic rituals at all and especially in the "pilgrimages" to the Tsaddiks on Saturdays and Holydays, the women's section of the Kloyz, if it existed, served only women living in the court, i.e. the family members and servants.
Kloyz of a powerful Hasidic leader, built in a similar form to the kloyz in Sadhora.
Asaf, David, Derekh hamalkhut: r. Israel miruzhin umekomo betoldot hahasidut (Jerusalem, 1997), pp. 367-373;
Austri-Dunn, Yeshayahu (ed.), Sefer yizkor lehantzhat kdoshei kehilat chortkov (Haifa-Tel Aviv, 1967);
Even Itzhak, Funem rebens hoif: zikhroines un maises (New York, 1922; reprint: Israel, 1970).