Following a turbulent period of family tragedy and heavy mourning, a profound shift occurred in King David's emotional state. The passage of time dulled the sharp pain of losing his murdered son, Amnon, making way for intense feelings directed at Absalom, the son who committed the murder and was now living in exile.
The primary approach among commentators is that David was consumed with a deep longing and yearning for his exiled son [רש"י, מצודת דוד, מצודת ציון, רלב"ג, ביאור שטיינזלץ]. This emotional pull was so powerful that his desire to go out to Absalom did not mean the king physically left the city; rather, it felt as though his very soul was leaving his body out of sheer desire to see him again [אלשיך].
Others suggest that a female figure was actively working behind the scenes to influence the king. One perspective proposes that this was Absalom's mother, who continuously pleaded with David until she awakened his longing and convinced him to send messengers to bring their son home [רד"ק].
A completely different reading views David's feelings not as longing, but as lingering rage. In this view, for three years David wanted to wage war against Absalom to avenge Amnon's murder, but he was held back. A female family member—perhaps his wife or his daughter Tamar—managed to contain his anger and prevent him from setting out to kill him. Alternatively, it was David himself who finally restrained his anger and put a stop to his servants' efforts to hunt down the fugitive [אברבנאל, מלבי"ם].
The root cause of this emotional shift was that David finally found comfort regarding Amnon. Commentators agree that David’s grief eventually settled because it is human nature to find comfort over the dead, who can never return [רש"י, מצודת דוד, ביאור שטיינזלץ]. While Amnon was gone forever, Absalom was still alive, and a person cannot find the same kind of closure for someone who is living but absent. Therefore, once the active mourning for the dead subsided, David's focus naturally shifted—either intensifying his yearning or lessening his need for revenge toward the son who was still alive [אלשיך].