Gemara

66b (Mishnah): The father and husband of a Na'arah (a girl in the first six months of adulthood) Me'orasah (after Kidushin but before Nisu'in) annul her vows;

If only one of them annulled the vow, it is not annulled. We need not say that if one affirmed the vow, it is not annulled.

Question: What is the Chidush of the Seifa?

If only one of them annulled, this does nothing. We need not teach that if one affirmed, the vow stands!

Answer: It teaches about when one annulled, and the other affirmed, and the one who affirmed went back and (asked a Chacham and) permitted his Kiyum;

One might have thought that he uproots his Kiyum. The Mishnah teaches that this is not so, both must annul together.

Rishonim

The Rif brings the Gemara verbatim.

Ramban: We conclude that he did not uproot his Kiyum. Rather, after he permitted his Kiyum, both must annul together.

Rambam (Hilchos Nedarim 13:21): If a Na'arah Me'orasah vowed and her father or husband affirmed it and the other one annulled it, even if he one who affirmed asked a Chacham and permitted his Kiyum, he cannot annul with the other. They can annul only together.

Ran (67a DH v'Chozar): They must annul at once, i.e. without any interruption in between that prevents Hafarah. If one affirmed it after the other annulled, the Hafarah is Batel. After permitting the Kiyum, both must annul together. This is like the Ramban. The Rambam disagrees. He holds that an Kiyum between Hafarah of one and Hafarah of the other permanently precludes Hafarah. However, they need not annul at the exact same time. If there was no interruption, surely even if one annulled in the morning and the other in the evening, it helps!

Keren Orah (67a DH Shuv): The Rambam did not discuss Kiyum in the middle (rather, when one affirmed before the other annulled)!

Note: Perhaps the Ran explains that the Rambam holds that because a Kiyum was in effect when the other annulled, the vow can never be annulled. The Kiryat Sefer says 'if the husband or father affirmed, he cannot permit this, because Kiyum of both of them is required.' Perhaps he explains that the Rambam teaches that Hataras Hakamah does not help even when we know that the other partner wants to annul.

Question (Keren Orah DH v'Chozar): Why should we say that it does not help even if both will annul later? If both affirmed, and permitted this, they could annul later. Why is it worse if one of them initially annulled?

Rosh (10:1): They must annul at once, i.e. without any interruption in between. E.g. when one of them affirmed it, he was unable to annul before permitting his Kiyum. Even if they will now annul together, it will not help. Some say that they can annul together now. The first opinion is primary. The Mishnah supports it. The Mishnah equates a case in which one of them affirmed, to a case in which one of them did not annul on the day he heard, and in the latter case, it can never be annulled.

Korban Nesan'el (2): The Rosh assumes that one did not annul on the day he heard. Surely, if both annulled on the same day without any interruption, even if one annulled in the morning and the other in the evening, it helps!

Question: Why does the Tana say '...we need not say that if one affirmed the vow, it is not annulled.' This teaches a Chidush, that Hafarah is Mevatel the previous Hafarah!

Answer (Ran, ibid.): Since he taught that if only one of them annulled, this does nothing, we understand that if one affirmed, the first Hafarah cannot join. If not, he would not say 'we need not say that if one affirmed...!'

Poskim

Shulchan Aruch (YD 234:6): If one of them (the father or husband of a Na'arah Me'orasah) affirmed, even if he permitted his Kiyum, he cannot annul it with the other.

Beis Yosef (DH v'Im): The Tur holds like the Rambam and Rosh.

Taz (7): Permission of Kiyum helps only regarding a Nesu'ah, since her husband annuls by himself.

Question (Gra 16): The Gemara discusses Kiyum after Hafarah. The Rosh and Ran explain that the interruption between Hafaros is Mevatel the first Hafarah. What is the source to say that permission does not help for Kiyum before Hafarah?!

Answer (Gra): The Shulchan Aruch is like the Rambam. The Rambam's text said that the first one affirmed. His text is correct. Our text says 'one annulled, the other affirmed, and the one who affirmed went back and permitted his Kiyum.' These words (the one who affirmed) are unnecessary. We were discussing him (he was the last one mentioned)!

Merumei Sadeh (67a): If one affirmed and permitted his Kiyum, both can annul afterwards. Hafarah is invalid if there was Kiyum at the same time. The Rambam's text says that Hafarah after Kiyum cannot join. Why didn't it teach about Hafarah before Kiyum? We must say that even a weak, Pasul Hafarah permanently prevents Hafarah, and all the more so a proper Hafarah that later became Batel through Kiyum. Our text says that Hafarah before Kiyum concerned join. We must say that they can always annul after the Kiyum was permitted; it is a bigger Chidush that this applies even after a strong Hafarah.

Question: Since a Chacham uproots retroactively, after the Kiyum is permitted, it should be as if it was never affirmed! We say so regarding Kidushin 'on condition that you have no Nedarim.' (If she had Nedarim at the time and later permitted them, the Kidushin takes effect - Kesuvos 74b.)

Answer #1 (Rashba 67a DH v'Kashya, cited by Beis Yosef DH v'Chosav ha'Rashba): The Gemara said 'one of them affirmed the vow', i.e. the father, the most important of the two. He has more power. E.g. if the husband annulled and the father died, the husband cannot annul by himself, but if the father annulled and the husband died, the father can annul by himself. Even though R. Noson says that this is like Beis Shamai, and Beis Hillel say that the father cannot annul, this is because the father weakened the vow, and the husband's authority is too weak to be inherited. The husband's Hafarah helps only when the father could annul.

Answer #2 (Ran, ibid.): Kidushin is a total action. Therefore, once the vow is annulled, it is revealed retroactively that the Kidushin took effect. Hafarah of one partner is weak. It does nothing by itself, and even with Hafarah of the other partner in a case when they cannot join, e.g. if the first died in the middle. Therefore, when the other affirms, the first Hafarah is totally Batel, and it can never help.

Question (ha'Granat, Nedarim 60): Hafarah of one partner does something! If the husband died, the father 'inherits' the husband's authority, and he can annul by himself. However, if the husband annulled before he died, he made the vow weak, so the father does not inherit the husband's authority!

Answer (ha'Granat): Hafarah of one partner does something only when it can join with Hafarah of the other. The Rambam holds that after permitting Kiyum, the vow is still weak due to the prior Hafarah (of the other party), therefore the other party cannot annul again. The Ran holds that once the Hafarah could not join, it was totally Batel, therefore he can annul again.

Answer #3 (Me'iri, and R. Avraham Min ha'Har citing Rashi): The Hava Amina was that permission of Kiyum is considered Hafarah. The Mishnah teaches that this is not so. However, indeed, after the Kiyum is permitted, the one who already annulled need not annul again.

Question (Keren Orah, ibid.): If so, the Mishnah should have taught permission of Kiyum is not considered Hafarah in a regular case when one person annuls by himself!

Taz (7) and Shach (15): The Beis Yosef and Darchei Moshe ha'Aruch (5) cite the Rashba, who says that the father's Kiyum is Mevatel the husband's Hafarah, but not vice-versa. None of the Poskim bring the Rashba, and the Shulchan Aruch itself does not make this distinction. Rather, we hold like the Ran; also Kiyum of the husband is Mevatel Hafarah of the father.

Shach (16): Even if he permitted his Kiyum on the same day, he cannot annul.