The Coalition is known as a participant of the historic War of Sol which culminated with the Alliance launching their escape from the Solar System.
The Great War
During the War of Sol, two blocs fought for complete control over the Sol System: the Alliance and the Coalition. The Coalition was composed of the communist nations of Russia, China, the Middle East, and Africa. For decades, constant fighting between the two factions ensued, with neither side gaining the upper hand for long.
In 2160, the Alliance proposed and signed a peace treaty between the two blocs, but as the Coalition admiral headed to Europa (one of Jupiter's moons) to sign it, he ordered a Coalition fleet to de-cloak and attack the Alliance fleet, who had stood down from battle after hearing about the treaty. Instead of ending the war peacefully, they destroyed the French and Italian fleets and took control of all the inner planets, including Earth, and most of the outer planets, excluding Neptune. Two years later, the Alliance recovered the outer planets and began its assault on the inner planets. Eventually, the Coalition was beaten back to Mercury. However, by some unknown means, the Coalition gained the upper hand and began to counterattack, eventually retaking every planet in Sol. During this counterattack the Alliance quickly built five Sleeper Ships and fled to what is now known as the Sirius System.
There has been no contact with the Coalition since the Sleeper Ships fled to the Sirius System. The Coalition has most likely become extremely powerful over the many years it has had full control of the entire Sol System, judging by the advanced technology it had already developed when the Alliance Colonists were only first arriving at Sirius.
Full article: Sirius Coalition
Although either denied or unproved by most sources, the Coalition is believed to have hidden saboteurs onboard the Alliance sleeper ships heading for Sirius, with their first successful act of sabotage being inflicting critical damage upon the sleeper ship Hispania, forcing it's inhabitants to eject early. Coalition agents are believed to have infiltrated all of the four houses to a degree, with their heaviest presence and support lingering in Bretonia and Rheinland.
However, even with this presence the forces loyal to the Coalition are in no way large enough to threaten the houses directly, and rather resort to terrorism or subtle sabotage to manipulate events that they believe are helpful to their cause. Even eight hundred years later, the descendants of the original saboteurs or the recruits rallied by them continue to fight for the idea of taking over the entirety of Sirius and rebuilding the Coalition with what's left.