Revenge
Absalom waited two years to get his revenge (or use revenge as a way to make clear his way to the throne.)
He asked King David to attended, probably knowing David would want his entourage to disrupt the events. Once David said 'no' it left Absalom the opening to ask David to send his heir in his place, Amnon. David seem to have an inkling that there was something amiss about this but approved it and send all of his sons. Maybe as a buffer between the two.
Wiersbe draws parallels between David's premeditated murder and escape with Absalom's premeditated murder and escape. Although David's sin was forgiven- the model had been given to the adult sons who were watching.
Revenge never solves anything. Nothing is better because of it. Specifically, Tamar was not better for it. Absalom thought he was better for it. Now he was in line for the throne. But that didn't work out either. Wiersbe: "The Christian way is the way of forgiveness and faith, trusting the Lord to work everything out for our good and His Glory (I Peter 4: 12-19.)"
Exile
Absalom fled to the land of his maternal grandparents. where his grandfather was king. Likely, he and his grandfather were planning how he could be king of Israel.
Meanwhile King David had grieved the loss of Amnon, but was comforted by time and began longing to see his living son, Absalom. Or the same verse can be interpreted that he had planned to go after Absalom and that had quieted over time.