Why does it say "va'Yhi Acharei Chen"?
Malbim: The Navi tells how were fulfilled the punishments that Nasan told David. After the baby died came the episode of Amnon and Tamar, which led to Amnon's death, and then the episode of Avshalom.
Why is she called Avshalom's sister?
Rashi: She was from the same mother. Radak citing Sanhedrin 21a - she was the daughter of a Yefas To'ar. The Torah permits one Bi'ah before conversion 1 ; she was conceived from this [so Halachically, she was not David's daughter]. A proof is, she told Amnon "the king will not withhold me from you" (verse 13). Later her mother converted, and Avshalom was born from her. Amnon called Tamar "my sister" (verse 6) because [biologically] she was David's daughter. Mahari Kara (6) - Tamar was captured with her mother, and later her mother converted and gave birth to Avshalom. 2
Tosfos (Kidushin 22a): According to Rashi, who forbids any Bi'ah before conversion, we must say that Tamar's mother was pregnant with her when David took her. Because she grew up in David's house with his daughters, she is considered like one of Benos ha'Melech (verse 18). She is called the sister of Avshalom and Amnon because they grew up together like siblings (Rashba 22a).
QUESTIONS ON RASHI
Rashi writes that Tamar and Avshalom had the same mother. Can we infer how old they were at this time?
Rashi (Melachim I, 3:7): Shlomo was born when Amnon raped Tamar - "va'Yhi Acharei Chen ul'Avshalom Achos
Bogeres is six months after becoming a Na'arah, after 12 years and two pubic hairs. It is feasible, but very rare, for a girl to delay 20 years before bringing hairs. If she were from a different mother, she could be about 12 years old; she is called Avshalom's sister because he avenged her shame, just like Shimon and Levi are called "Achei Dinah" (Bereishis 34:25). However, here he is called so before he did anything! Also, Radak, R. Yeshayah, Abarvenel, Yad Ramah (Sanhedrin 107a) Me'iri (Kidushin 22a) and others say like Rashi, and I did not see anyone disagree. (PF)