I want to address the bit about Absalom. David was very clear to tell Joab NOT to kill his son. He wanted him captured, but not killed. David's love for his erring boy is much like God's love for us. Even though Absalom had done a lot of evil things, and rebelled against his father, David wanted to have him back with him. When the courier came with good news, David immediately wanted to know if his boy was safe- that would have been good news to him.
II Samuel 18: 28-33 "And Ahimaaz called, and said unto the king, "All is well." And he fell down to the Earth upon his face before the king, and said, "Blessed be the Lord thy God, which hath delivered up the men that lifted up their hand against my lord the king." And the king said "Is the young man Absalom safe?" And Ahimaaz answered, "When Joab sent the king's servant, and me thy servant, I saw a great tumult, but I knew not what it was." And the king said unto him "Turn aside, and stand here." And he turned aside and stood still. And behold, Cushi came; and Cushi said, "Tidings, my lord the king: for the Lord hath avenged thee this day of all them that rose up against thee." And the king said unto Cushi "Is the young man Absalom safe?" And Cushi answered "The enemies of my lord the king, and all that rise against thee to do thee hurt, be as that young man is."
And the king was much moved, and went up to the chamber over the gate, and wept: and as he went, thus he said "O my son Absalom, my son, my son Absalom! Would God I had died for thee, O Absalom, my son, my son!"
I don't think David was much interested for getting vengeance for Absalom's betrayal. He would have rather died than have his precious son die. People ask why David was a man after God's heart. Here is one reason why. How many kings were ruthless when it came to power? Killing relatives willy nilly to retain the crown. David would have rather been defeated and died than to have his son die. Joab even upbraids him for "loving his enemies and hating his friends".
Long story short, I don't believe the imprecatory psalms are against Absalom.