Absalom's return to Jerusalem is not a full reinstatement to royal favor, but rather a conditional arrangement marked by severe restrictions. The king imposes a strict protocol that prevents Absalom from resuming his natural status, expressing instead a deep sense of distance and reservation.
The king's directive consists of two clear conditions [מלבי״ם]. The first governs exactly how Absalom is to enter the city. At a basic level, he is simply ordered to head directly to his own house [ביאור שטיינזלץ]. However, this requirement carries a much heavier restriction. Unlike typical royalty returning from a distant journey, Absalom is forbidden from marching down the main street with joy, public honor, and musical accompaniment. Instead, he must take a winding route, circle the city, and slip into his home through hidden, unpublicized paths [מלבי״ם, אברבנאל]. The purpose of this quiet arrival is to prevent him from appearing in public with pride and arrogance, particularly in light of the severe sin he had committed [אברבנאל].
The second condition dictates a complete severing of their personal relationship. The king explicitly declares that he has no desire to see Absalom at all [ביאור שטיינזלץ, אברבנאל]. Complying with these firm orders, Absalom retreats to his own home and lives in isolation, entirely cut off from the king's presence.