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The Gaon R. Akiva Eger discussed a similar issue in response to a scholar whose daughter was quite ill, so much so that all food was harmful to her, and for many weeks she had been living on medicines. The question was whether she was required, according to Halacha, to eat on Erev Yom Kippur (Responsa by R. Akiva Eger, 16).
R. Eger answered, “Chalila vechalila – Heaven forbid that she should eat. And since you write that she is learned, very observant and G-d-fearing, she will probably, though very reluctantly, listen to you.
“My advice is that you should take one or two individuals along with you to tell her that this letter of mine contains the following ruling in her regard: she is not allowed to eat anything more on this day than she would on any other day.”
He continues, “I am a bit confused as to whether women [who are not ill] are required to eat on Erev Yom Kippur. [Obviously they will eat in preparation for the fast of Yom Kippur, but are they actually required to eat?] Perhaps they are relieved from this mitzva as in all other situations of mitzvat aseh sheha’zeman grama – a time-driven mitzva.’”
“Note as well that the Kesef Mishneh commenting on (Hilchot Shevitat Asor 3:9) ponders whether the exegesis of ‘Ha’ochel veshoteh ba’teshi’i … – He who eats and drinks on the ninth is considered as if he fasted both on the ninth and on the tenth,’ is a solid, steadfast exegesis or whether it is only an asmachta – a supporting source – and thus it would only be a mitzva that is time-driven and women are relieved of that requirement. Or perhaps this is not so, since the verse states ‘On the ninth day of the month in the evening,’ to teach us that it is considered as if they fasted on both the ninth and the tenth, and whoever is required to fast, women included, are also required to feast (eat) on Erev Yom Kippur.”
Thus we see that even according to R. Akiva Eger it would seem that we might find reason to require a healthy woman to eat on Erev Yom Kippur due to doubt about the requirement, and he is lenient only in the case of a woman who is seriously ill.
Regarding the requirement for women to eat in the sukka, the Mechaber (Orach Chayyim 640), based on the mishna in Tractate Sukka 28b, rules that women are not required to perform that mitzva.
Yet the Mishna Berura (ad loc.) states that while they are exempt from this obligation, if they choose to eat in the sukka and wish to utter the blessing “leishev basukka,” they must do so themselves; a man may not do it for them. (This means that if the man already ate he may not recite this blessing solely for the woman who did not eat yet – see Ba’er Heitev ad loc.)
The Rema (Orach Chayyim 589) states as follows: “The custom is that women bless on mitzvot aseh sheha’zeman grama,” disputing the Mechaber, who rules that they do not.
Thus we see that even though there is no Biblical mitzva for women to eat in the sukka, there is a halachic precedent. Additionally, the greatest simcha on Yom Tov is when the entire family sits down and enjoys the Yom Tov meals together. Since men must eat in the sukka, it logically follows that the women will eat there as well – but only at their discretion.
However, there are many Chassidim who are very strict that women do not eat in the sukka. The men make Kiddush aloud and the women stay outside the sukka and listen. It is possible that your wife comes from such a family. Usually, a couple follows the husband’s customs. What is unique here is that eating in the sukka is a custom that is dependent on the woman; it is her prerogative.
However, for shalom bayit purposes, you may try to gently persuade your wife to sit with you in the sukka, at least in your home. Understandably, when you are at her parents’ home, it would be proper for you to abide by their customs.