David did not see Avshalom take David's Pilagshim!
Radak: Even if you would know, you would not be able to stop it. It is as if it is in front of your eyes.
Why does it say "l'Re'echa"? Avshalom was his son!
Radak #1: It means one of your beloved. There is no greater beloved than one's son!
Radak #2: It is someone who wants to be as if he is your equal, regarding kingship.
Why does it say "l'Re'echa (plural)"?
Radak #1: It is singular. The Yud is the last letter of the root.
Radak #2: It will be to one of your Re'im, i.e. one of your beloved.
What is the meaning of "your wives"?
Radak: Your Pilagshim.
What is the meaning of "l'Einei ha'Shemesh"?
Radak: It is openly; Avshalom entered the tent with them.
Did Hashem decree that Avshalom sin due to David's sin, and if not for David' sin, Avshalom would not have sinned?
Radak: Hashem did not decree that Avshalom sin; He did not mention his name. Hashem knew that it will be Avshalom, due to his lust to sin. Had David not sinned, Hashem would have prevented this. Even though Avshalom was destined to sin due to his lust, it would not have been with David's wives. 1
Radak citing Rav Sadya Gaon: There were two parts to this Nevu'ah. Hashem decreed "Hineni Mekim Alecha Ra'ah", that Avshalom will rule over everything of David. "V'Shachav Im Nashecha" was through Avshalom's choice. Hashem informed David what will depend on his choice.
Radak: This was not such a great sin, since they were only Pilagshim. One may marry Mefutas Aviv (a woman with whom his father had Bi'ah, without Kidushin. This is like the opinion that Pilagshim have no Kidushin (refer to Shoftim 8:31:1:1,2 and the notes there). However, since they were a king's Pilagshim, they were forbidden to everyone else, and all the more so to his son it is repulsive.