Before one eats in the Sukka at any point during Sukkot, he recites the Beracha "…Asher Kideshanu Be’misvotav Ve’sivanu Lesheb Ba’sukka." Sephardic practice follows the view of the Shulhan Aruch that women should not recite this Beracha. Since women are exempt from the obligation to eat in the Sukka, they cannot say the words "Ve’sivanu Lesheb Ba’sukka" ("and He commanded us to sit in the Sukka"). Even though women have generally taken it upon themselves to eat in the Sukka, the fact remains that they are technically exempt from the obligation, and therefore, according to Sephardic tradition, they do not recite the Beracha.
This Halacha gives rise to an interest dilemma when Kiddush is recited in the Sukka. On Yom Tob and Shabbat Hol Ha’mo’ed, when the husband recites Kiddush, he recites the Beracha of "Lesheb Ba’sukka" as part of the Kiddush. Should a woman answer "Amen" to this Beracha? Since, as mentioned, women themselves do not recite this Beracha when they eat in the Sukka, this Beracha bears no Halachic relevance to them. Seemingly, then, if they answer "Amen" to this Beracha, they will have made an interruption in between the Beracha recited over the wine ("Gefen") and their drinking of the wine. As we know, the common practice is for the wine to be passed around the table after Kiddush, and for everyone to drink some wine without reciting a Beracha, relying instead on the Beracha they heard from the one who recited Kiddush. If, however, the woman answers "Amen" to the Beracha of "Lesheb Ba’sukka," she has perhaps made an interruption, such that the Beracha over the wine that she heard can no longer cover her drinking.
Indeed, for this reason, Hacham Ovadia Yosef ruled that women should not answer "Amen" to the Beracha of "Lesheb Ba’sukka" recited as part of Kiddush. They certainly answer "Amen" if they hear this Beracha recited in other contexts, but in the context of Kiddush they must not answer "Amen," for the reason discussed. Hacham Ovadia drew an analogy between this situation and a comment made by Rav Isser Zalman Meltzer (Lithuania-Israel, 1870-1953) regarding Habdala. There is a common practice for women not to drink from the cup of wine at Habdala. Rav Isser Zalman suggested that the reason for this custom perhaps relates to the view of some authorities that women are not obligated in Habdala. Habdala consists of several Berachot; it begins with the Beracha over the wine, followed by the Berachot over the spices and the candle, and, finally, the Beracha of "Ha’mabdil." If a woman is exempt from Habdala, then the Berachot recited after the Beracha over the wine have no Halachic relevance as far as she is concerned. As such, her responses of "Amen" to these Berachot would constitute an interruption in between the Beracha over the wine and her drinking, and she would have to recite the Beracha herself. The custom therefore emerged that women do not drink from the Habdala wine, as they might otherwise drink without reciting a Beracha.
Similarly, Hacham Ovadia writes, women should not answer "Amen" to the Beracha of "Lesheb Ba’sukka" recited in the context of Kiddush, for if they do, they will have to recite their own Beracha of "Gefen" over the wine.
Summary: The custom among Sepharadim is for women not to recite the Beracha of "Lesheb Ba’sukka" before eating in the Sukka. If they hear a man recite the Beracha, they may and should answer "Amen," except when this Beracha is recited as part of Kiddush, in which case they should not answer "Amen."