Who is Eglah?
'Rashi', from Bereishis Rabah 82:7: It is Michal. She screamed [amidst her birth pangs] and gave birth to him. 1 Also, she was dear to him like a calf. Also in Shofetim (14:18, this refers to a wife) "Lulai Charashtem b'Eglasi." 2
Radak (Shmuel II, 3:5) #1: It is a different wife. Michal is not mentioned here, for she did not have a son. Here the Torah lists David's sons, and with them, their mothers.
Radak (Shmuel II, 3:5) #2: She was Sha'ul's wife. 3 David married her after Sha'ul died ? "v'Es Neshei Adonecha b'Cheikecha" (Shmuel II, 12:8). Even though one may not marry a king's widow, a king may marry a king's widow (Sanhedrin 18a).
Our version of the Midrash says 'and died', like the opinion that she died on the day that she gave birth (Refer to 3:3:3:2 - PF).
Also Rashi (Shmuel II, 3:3, from Shochar Tov 59) brought the latter Perush. Also Vilna Gaon and Malbim say that she is Michal. Radak (ibid., 5:13) - Sanhedrin 21a was forced to say so, for we learn that a king may marry only 18 wives from "v'Osifah Lecha ka'Henah vecha'Henah" (Shmuel II, 12:8; another six and another six.), so we must say that Michal was among the six listed.
Radak: Even though she was the wife of David's father-in-law (she was not his mother-in-law; Michal was from a different wife of Sha'ul), one may marry his father-in-law's wife. The Yerushalmi (Yevamos 2:4) forbids, but this is only mid'Rabanan due to Maris ha'Ayin. It says that David married Ritzpah, Sha'ul's concubine, for a wife. (According to the opinion that a concubine has Kidushin (refer to Shofetim 8:31:1:1,2 and the notes there), she is like a wife regarding Arayos.) R. Meir Simchah (on the Yerushalmi) ? since the Isur is only due to Maris ha'Ayin, it was permitted due to Agunah (a king's widow can marry only a king. If she may not marry David, she cannot marry anyone!) This is unlike the Bavli (Yevamos 21a) which says that Shlomo decreed Sheniyos (Arayos mid'Rabanan. If so, there is no question from David! ? PF)
Why is only Eglah called Eshes David?
'Rashi': It is because she was so dear to him.
Radak: She was [Michal,] his first wife.
Radak (Shmuel II, 3:5) #1: (She was not Michal.) She was not from a great family, so she is not called by her family's name, rather, Eshes David.
Radak (Shmuel II, 3:5) #2, according to R. Yehudah (Sanhedrin 18a): She was Sha'ul's widow. She could not be a wife to anyone else, only to David, for only a king may marry a king's widow.
Vilna Gaon: (She is Michal.) The verse teaches that she was his full wife. She was not forbidden to David through being given to Palti ben Layish (he never had Bi'ah with her), and not due to Achos Ishto, for he married her six months after her sister Meirav died. Also, David's Kidushin of Meirav was via a loan (and invalid).
Malbim (Shmuel II, 3:5): This is Michal; she was proper for David, for she was a king's daughter.
QUESTIONS ON RASHI
Rashi writes that "Eglah" is Michal. Shmuel II, 6:23 says that she did not have a child until the day she died!
Radak, from Sanhedrin 21a: She did not bear a child from that episode 1 and onwards. This was her punishment for despising David. Before that, she had a child.
Radak (Shmuel II, 3:5) citing Sanhedrin 21a: She had a child only on the day that she died. 2
Radak (Shmuel II, 6:23 citing Bereishis Rabah 82:7): Three died amidst birth, - Rachel, Eli's daughter-in-law and Michal.
