Star Wars: Birth of the Republic
Coruscant and Allies
When Tython joined the free worlds in an attack against an Infinite Empire fleet garrisoned above Coruscant, which was then their client world, Coruscant rebelled against their Imperial masters, depriving the Empire of their ability to rearm and refuel and capturing a number of planetary defenses, which were then turned against the Empire. In the fires of that battle, a strong alliance between Coruscant and Tython was forged.
The addition of Alsakan to that power bloc was more recent, but has catapulted the alliance to being the single most powerful political player in the free worlds in terms of both military and economics. Coruscant and Alsakan’s initially shaky alliance was funded on their mutual desire to end the conflict with the Infinite Empire (as opposed to Corellia, who advocated that all pockets of resistance be hunted down and crushed before they could regroup), a focus on the future, and most pressingly, a mutual need to colonize the Perlemian Trade Route and beyond in order to break out of the small patch of space the two worlds have found themselves locked into. With the only route west threatening to bump into the Infinite Empire’s heartlands and reignite the war, and the routes to the south already monopolized by the Duros, Coruscant and Alsakan both find themselves needing access to the Perlemian Trade Route if they want to remain galactically relevant.
Coruscant was used as the Infinite Empire’s main base of operations during initial attacks against the rebelling slave worlds, and was most notably the staging area for devastating attacks on Kuat when it was first gripped by rebellion. Thus, though they were initially colonized by Coruscant, Kuat maintains chilly relations at best with the Alsakan/Coruscant alliance. Likewise, though Corellia is more than willing to cooperate with Coruscant, they have little love for them, as they were both one of the last worlds to rebel and one of the ones who suffered the least under the yoke of Imperial rule.
Alsakan is basically adjacent to the Azure Imperium, which makes them nervous about the potential for invasion from the saber-rattling Azurites. Militarization of Alsakan in response to Azurite rhetoric is seen by the Azure Imperium as evidence that war between the free worlds is indeed inevitable, which leads the Azure Imperium to build up their own military, resulting in a cycle of military build-up that some say can only be broken by war.
Being on the other side of the known galaxy from them, the Duro Kingdom cares about Coruscant and Alsakan primarily as trade partners, since they control between them the gateway to the north and west of the galaxy and that’s going to be really important if anyone ever starts colonizing those areas. So while Duro maintains friendly relations with them, they wouldn’t go to war on their behalf (except perhaps if the Infinite Empire were on the other side). Alsakan, however, sees the expanding colonial empire of the Duros as a threat to their galactic relevance, fearing they may sink into a backwater as the Duro Kingdom expands. This fear has rubbed off on Coruscant.