Gemara

109b (Mishnah - R. Gamliel): If she does Mi'un (if not, she waits until she grows up, and then her older sister is exempt).

(Rav): R. Gamliel holds that (now, a new act of) Kidushin of his Yevamah's sister exempts his Yevamah from Yibum and Chalitzah. This is only through Bi'ah after she matures.

(Rav): If a minor did not do Mi'un, and she married David (another man) after she matured, she does not need a Get from David;

(Shmuel): She needs a Get from David.

The case is, she had Bi'ah with her first husband (Reuven) after maturing. Shmuel does not require a Get because he holds that when Reuven has Bi'ah, he relies on the initial Kidushin (and does not intend to Mekadesh through Bi'ah).

Question: The following shows that Rav says that she is married even without Bi'ah!

A case occurred in which David was Mekadesh Leah (mid'Rabanan), she matured, and she was sitting by the Chupah. Levi grabbed her (and was Mekadesh her). Rav Beruna and Rav Chananel, Talmidim of Rav, were there, and they did not require her to get a Get from Levi.

Answer (Rav Ashi): Since Levi acted improperly, Chachamim acted improperly to him (and uprooted his Kidushin).

Gitin 89b - Question (Bei Rav): If there were rumors that Reuven was Mekadesh Leah, and then Shimon was Mekadesh her with witnesses, and the rumors were found to be unsubstantiated, what is the law?

Answer #1 (Rav Huna): Reuven divorces her, and she marries Shimon. We do not allow that Shimon divorce her and she will marry Reuven.

We are concerned lest people say that the rumors were true, Reuven divorced her, and now he is Machazir Gerushaso after she became Mekudeshes to another man.

Answer #2 (Rav Shinena brei d'Rav Idi): She may even marry Reuven after Shimon divorces her;

People will say that Chachamim investigated and found that Shimon's Kidushin was invalid.

Nidah 46a (Rav Dimi of Neharda'a): The Halachah is, (a girl above 12 may not do Mi'un even if we see that she does not have hairs now;) we are concerned lest she brought hairs after 12 years, and they fell out.

This is only if she had relations with her husband after 12, for then it is a Safek mid'Oraisa. If not, we are not concerned.

Rishonim

Rif and Rosh (13:7): If David was Mekadesh her, it takes effect. It seems that if David wants to have Nisu'in with her, Reuven divorces her and she marries David. However, she may not marry Reuven after David divorces her, like it says in Gitin when rumors (of Kidushin to Moshe) were found to be unsubstantiated (and Yakov was Mekadesh her). We are concerned lest people say that Moshe divorced her and is Machazir Gerushaso after she became Mekudeshes to Yakov. The same applies here.

Nimukei Yosef (DH Gemara): If she had Bi'ah with her husband (Reuven) after maturing, she does not need a Get from David. Some say that this is only if she did not accept Kidushin in front of Reuven. If she did, she needs a Get from David, for this is like saying to her husband that he divorced her. Rav Hamnuna taught that she is believed, for a woman lacks the audacity to say such a lie to her husband. However, some say that here is different, because she thinks that her first Kidushin was invalid, for it was initially Safek and now she does Mi'un, but really she cannot do Mi'un now.

Rif and Rosh (ibid.): This is only if David did not have Bi'ah with her before Reuven divorced her. If he did, she is forbidden to both of them and needs a Get from each of them, like a woman whose husband returned after she remarried after hearing that her husband died. However, the children are not Mamzerim, for the first marriage was only mid'Rabanan.

Question (Ra'avad, brought in Rosh, ibid.): We can rely on the Rif even if he forbids what is permitted. It seems that the fines were only for one who transgressed Ervah or a Lav mid'Oraisa. Here there is neither. If someone permits, we heed him.

Answer (Sefer ha'Zechus): The fines apply even to one who married with a Get that does not comply with enactments mid'Rabanan, e.g. if it was dated according to the reign of Romi or was not signed where it was written or if a Get Mekushar has more folds than signatures. All the more so we are stringent here, for she was Mekudeshes to the Rishon!

Rebuttal (Rosh): Chachamim enacted to fine one who remarried with a Get unlike their guidelines. There was no enactment about one who remarried without Mi'un. It is merely a fine because he transgressed. We cannot Mechadesh new fines without a source.

Support (for Rosh - Gra EH 155:74 and 10:5): The Yerushalmi (14:1) says that since there is not even Asham Taluy for a Cheresh's wife who was Mezanah, if she became Mekudeshes to another and was divorced, she may return to her first husband.

Sefer ha'Zechus: Some say that if David did not have Bi'ah with her she is permitted to both of them, for people will assume that it was mistaken Kidushin. This is wrong. We say so only when there was Safek Kidushin.

Ramban (110a DH Rav): Rav Ashi ruled like he holds (Bava Basra 48b) that if one forced any woman to accept Kidushin, Chachamim uprooted the Kidushin. Alternatively, (she was not forced;) here he discusses only one who did not do Mi'un. Chachamim want her to stay with her husband, lest she be treated like Hefker.

Nimukei Yosef (ibid): The Ritva says that if she had Nisu'in with David, since it is Nisu'in mid'Oraisa and she needs a proper Get, all 13 fines apply, for she looks like a woman whose husband returned after she remarried based on one witness. This is only if from the beginning she married him willingly. If initially she did not want him, even if she did in the end, it is not Kidushin. We learn from the case of the man who grabbed a girl by the Chupah. We must say that her in the end she agreed to Kidushin, for otherwise we would not need to say that Chachamim uprooted her Kidushin. We concluded (Bava Basra 48b) that if one was forced to Mekadesh or accept Kidushin, it is invalid. If she was willing from the beginning it is valid. We find that if Reuven was Mekadesh Leah through Bi'ah and she accepted Kidushin from David in the middle, she is Mekudeshes to David (if the end of Bi'ah acquires). Even though David acted as improperly as can be, since Leah consented from the beginning Chachamim did not uproot his Kidushin.

Rambam (Hilchos Gerushin 11:5): If a girl did Mi'un after she was checked (and found not to have Simanim) and became Mekudeshes to David (another man), she needs a Get due to Safek. If she had Nisu'in with David, she must leave both men, and children from both of them are Safek Mamzerim.

Rambam (6): If she became Mekudeshes to David after maturing, Kidushin takes effect. If her husband (Reuven) divorced her she may marry Reuven. However, if David divorced her she may not marry Reuven, lest people say that he was Machazir Gerushaso after she became Mekudeshes. If David had Bi'ah with her before Reuven divorced her she must leave both of them because she resembles a woman whose husband returned after she remarried after hearing that her husband died. Her children from David are not Mamzerim. If she had a child from Reuven before David divorced her, the child is a Mamzer.

Mishneh l'Melech and Beis Yosef DH Kosav ha'Rivash: The Rivash (Sof 193) cites the Ro'oh who says that we do not need Edei Yichud (witnesses who know that she was secluded with Reuven for Bi'ah). Since she is his wife and they live together, all know that they were secluded and he had Bi'ah with her. The Rivash himself (Sof 6) disagrees and calls this an individual's opinion. All other Rishonim require Edei Yichud.

Poskim

Shulchan Aruch (155:20): If a girl did Mi'un to Reuven after having Bi'ah with him after 12 years and she was checked and no hairs were found, if David was Mekadesh her she needs a Get from Reuven mi'Safek. She may not return to Reuven. If she had Nisu'in with David she must leave both of them, and the child from either of them is a Safek Mamzer.

Beis Shmuel (31): The child from either of them is a Safek Mamzer mid'Oraisa.

Shulchan Aruch (21): If she brought two hairs after 12 years and did not have Bi'ah with Reuven after this, this is Safek Kidushin. If he did not divorce her and she became Mekudeshes to David, she needs a Get from both. She may marry David after Reuven divorces her, but she cannot marry Reuven after David divorces her, lest people say that he is Machazir Gerushaso after she became Mekudeshes.

Beis Shmuel (33): Whenever the latter Kidushin was forbidden, we are concerned for suspicion. This is unlike a Yevamah who became Mekudeshes l'Shuk. There, she is forbidden to the Mekadesh, for he transgressed mid'Oraisa. The Ri'az (in Shiltei ha'Giborim 38a) says here that David divorces her and she may marry Reuven, for a sinner may not profit.

Beis Yosef (DH u'Mah she'Chosav Afilu): The Rif, Rambam and Rosh do not discuss one who grabbed a girl from the Chupah and was Mekadesh her. It seems that they hold that the Halachah does not follow Rav Ashi. Even though he is Basra, perhaps he merely explains why Rav's Talmidim did not require a Get, but he himself disagrees.

Shulchan Aruch (ibid.): If she had Bi'ah with David before Reuven divorced her, she must leave both of them. The child from David is not a Mamzer. If she had Bi'ah with Reuven before David divorced her, the child is a Mamzer.

Source (Gra 75): The child from David is not a Mamzer because even regarding a Get that is Pasul mid'Rabanan, only R. Meir makes the children Mamzerim (Gitin 80b).