Why did he say "Al b'Apecha Sochicheni"?
Radak: If You will rebuke me for my sin, do not do so with anger. Do so slowly, so I can bear it - "Yasereni Hashem Ach b'Mishpat" (Yirmeyah 10:24).
Malbim: Af is exposed anger. Chemah is hidden anger and hatred. Sometimes there is Af without Chemah - one shows an angry face, but there is love in his mind. There can be Chemah without Af if he hides his anger. There is also a difference between Tochachah and Yisur. Tochachah is with soft words; Yisur ties the Nefesh with harsh matters, or literally afflictions. Hashem's Tochachah for sin is sometimes lest the person sin in the future. David requested that it not be with anger, rather, with soft words, like a father to his son. He did not need to request that it not be with Chemah and bearing hatred, for an enemy does not rebuke or try to make one return to the good path. Open rebuke is always from hidden love.
Why did he say "v'Al ba'Chamascha Seyasereni"?
Radak: The matter is repeated in different words, like is common.
Malbim: Sometimes Hashem brings afflictions for a sin. These must be with Af, to show His anger. David asked that at least, they should not be with Chemah, like an enemy that afflicts. Rather, "Ka'asher Yeyaser Ish Es Beno Hashem Elokecha Meyaserecha" (Devarim 8:5), "v'Ohavo Shicharo Musar" (Mishlei 13:24).
