What you are describing very closely resembles feudal Europe. Lack of reliable communication and transit meant that local lords were very autonomous in their day to day activities allowing them a lot of freedom go out raiding and fighting among themselves, but everyone was sworn to a lord who was sworn to a higher lord who after so many layers was sworn to a king which the most of the nobility rarely ever heard from but obeyed without question. The king only ruled a very small part of the country directly, but indirectly everyone was sworn to him through the feudal chain of command making him too powerful to challenge.
Feudalism works best when each lord only has the ability to effectively control lands within a certain proximity of his home, these divisions of land were typically called counties or parishes. In medieval Europe, poor roads and lack of good communications systems typically limited a county to a town and the surrounding farms and wilderness. In your space civilization, it could be that interstellar travel and communication is hard or time consuming enough that planets or solar systems only make sense to be locally governed. Either way, because lands beyond a certain point take too long to exchange communications with, it's very hard for a lord to govern what happens too far away.
Since each territory is surrounded by other territories, no one county can safely stand on their own so they will need to form alliances. The lords of each county will tend to flock to the most powerful other county in their region for protection by swearing loyalty in exchange for that protection. The more loyalty a count can garner, the more absolute his power over the region becomes until eventually he established a larger division of power where everyone who lives in his shadow is forced to swear loyalty or be conquered by the combined force of this alliance. These larger areas are typically called duchies.
As these duchies start to form you will start to see a lot of adjacent dukes start going to war over disputes about who should have the vassalship of certain border counties; so, they start to find themselves in the same condition as before of being surrounded by too many enemies. These dukes then form even larger alliances where a powerful duke begins amassing the loyalty of other dukes.
Depending on how large your feudal kingdom is, this process may repeat itself many times and create a complex system of alliances resulting marquis, earls, viscounts, barons, etc. Regardless of how complex the system gets there is always going to be one guy at the top of this pyramid scheme. This is king Ar'axhir.
On its own, Artarkan may not be the strongest planet in the kingdom, but it is at the center of this complex system of loyalties, and that makes it the strongest world.
Limited fighting and warring between the clans is both tolerated and to be expected by the Artarkan, because they understand that this is a natural part of lords vying for greater positions in the upper courts. Intervening in these conflicts would often mean dispatching forces over very long distances; so, the king and higher lords generally only involve themselves in a conflict when it escalates enough to threaten their own power; otherwise, these "quarrels" are just seen local matters for the lesser lords to deal with.
Ultimately, this means that the ruler of the empire does not own the hundreds of other worlds in his kingdom, and he must be careful to tread lightly when it comes to telling them what to do, but as long as he maintains these loyalties well through close relationships with the uppermost lords who are sworn to him, he can muster enough of the kingdom's strength whenever needed to exorcise his supremacy and re-establish order whenever things get out of hand.
This means that local lords seeking to gain power won't risk doing so by raising large armadas and trampling dozens of worlds under foot, even if they have the power to do so. Instead, they rely on things like isolated raids and state sponsored piracy, to undercut their rivals' power and obfuscate culpability.