1. Relations
Luminai
All Cassians are loyal to a Cassian High Family. The High Families are in turn loyal to one of the Seven Great Houses of the Luminai.
Mechari
As Eldan creations, Cassians revere the Mechari and generally follow their advice without question.
Chua
Cassians feel that Chua provide an indispensable service to the Dominion, and usually overlook their mischievousness because of it.
Draken
Cassians respect the skill and ferocity of the Draken, seeing them as the ultimate manifestation of Dominion strength.
Exile Humans
Cassians harbor an intense hatred of their Exile brethren, consider them unforgivable traitors and heretics.
Aurin
Cassians consider Aurin little more than feral forest creatures whose presence is a desecration of their rightful kingdom.
Granok
Cassian humans will never forget the Granok and the embarrassing defeat the Dominion suffered against them. They look forward to settling the score.
Mordesh
The Cassians see the Mordesh as foul, diseased abominations worthy only of extermination. They will usually attack them on sight, in order to destroy them before they spread the Contagion.
Source: Loremageddon2. Mercenaries
The Dominion prefers to use its own troops. That said, it has been known to hire mercs on occasion for special reasons.
Source: Twitter3. Terrible things the Exiles do
What the Dominion sees as terrorism, essentially - sneak attacks, targeting non-military structures, even dismantling Mechari. And at the start of the war, the Cassian rebels (not yet Exiles) plowed a furrow of mega-death through the Cassian navy's fleet, killing thousands and almost causing them to lose control of the empire from lack of ships. What Exiles might see as mean, many in the Dominion see as forceful and necessary, albeit sometimes regrettable. Of course, there's also plenty of hate and bile on both sides. They're not nice to each other in general.
Source: Reddit4. At war with
We have yet to meet a lot of other galactic powers, and it's safe to say that few are as organized, ambitious, or focused as the Dominion is on governing vast swaths of the galaxy in an orderly manner. The Eldan chose the Cassians for a reason, including the fact that they already had a Commonwealth of planets and showed the potential for wise interstellar government. Militarily, think of it as the Roman Empire (perhaps not surprisingly) - they keep that army so they can use it but they also keep a lot more than they might need to take on other cultures in hopes, perhaps, they can win battles without ever fighting.
The war against the Exiles has surprised many within the Dominion simply by going on as long as it has - but that's because an entity like that has trouble fighting smaller, scrappier, more mobile forces that can adjust their tactics on the fly. All that said, the Dominion definitely has to deal with - or at least have the strength to deal with, if necessary - the Marauders, the Krogg of the Darkspur Cartel, and the mysterious Ikthians (who are a whole 'nother ball of fish).
Then there's the Great and Benevolent Rowsdower Federation. But we don't talk about them.
5. The bigger threat: Ikthians or Exiles
While the Dominion considers the Ikthians to be a species of dangerous trespassers on Nexus, the empire’s day-to-day efforts are almost completely focused on defeating the Exiles. Until such time as the Ikthians can successfully prove to the Dominion that they are more than an occasional nuisance, the Exiles will continue to be its primary concern.
6. Why Arboria was never given a chance by the Dominion
Harboring the enemies of the Dominion is more than enough for the empire to justify its actions. Ignorance is no excuse in the eyes of Dominion law. Plus, the Exiles likely told the Aurin about the Dominion.