A man on the run faces not only the struggle of his own survival but the heavy burden of protecting his vulnerable loved ones. Constantly fleeing from Saul, David is forced to seek a secure refuge for his elderly parents. His family had originally fled to join him because Saul's intense hatred extended to them as well, creating a real fear that the king would exact revenge upon them and put their lives in danger [רד״ק, ביאור שטיינזלץ].
To secure their safety, David turns to the king of Moab for asylum. This specific choice was likely rooted in his historical family ties to Ruth the Moabite, the matriarch of his lineage [ביאור שטיינזלץ]. David's goal is to remove his parents from their temporary and hazardous hiding places. Whether they were taking shelter in the cave of Adullam [רד״ק, מצודת דוד] or stationed in a military fortress vulnerable to the dangers of war, he wants to transfer them to the safety of the royal city [מלבי״ם]. While his parents are sent away for their protection, David's brothers do not relocate to Moab. Instead, they remain behind to continue wandering alongside him [רד״ק].
David asks for this protection to last until he can understand what God has planned for his future. This period of waiting is understood in two distinct ways. It may mean that David is simply biding his time until he can secure a permanent and safe home where his parents can eventually return and live with him [מצודת דוד]. Alternatively, it reflects David waiting to see how God's justice will unfold to avenge him against Saul, a man who had repaid his loyalty and goodness with evil [חומת אנך].