“and went to Talmai…king of Geshur.” Absalom fled out of Israel to his maternal grandfather, who had a marriage alliance with David and who protected him. The marriage of David and Talmai’s daughter is in 2 Samuel 3:3, but see commentary on 2 Samuel 3:2.
“David mourned for his son every day.” The Hebrew is “he mourned for his son,” but “David” is inserted for clarity. But what “son” is David mourning for, Amnon or Absalom? This is a difficult question because the word “son” is singular. David did miss Absalom (2 Sam. 13:39, 14:1).