[OOC —
The trouble is twofold for the Commonwealth to support Omi's Southern Court. One, and I am sure the TH would love this, it would give political ammunition to Skye, even if the cause of Skye has been set back for at least 2-3 decades, and second, conspiring with traitors to the Dragon? Well, now isn't that going to offend the Dragon's honor as well?
Personally, I don't see the Hegemony making much of a fuss over the LC or anyone supporting Omi. It is a case of apples and oranges—quite honestly—in comparison to Skye, and one the Hegemony probably supports. Keep in mind that each nation is its own distinct entity and approached differently. So Terra selling arms to Skye separatists and supporting Omi might create domestic problems for said nation, but achieve very different ends in very different years. The same could be said if the Commonwealth did the same...the "enemy of my enemy"....etc. Either way, it's the Commonwealth responding to specific players and a specific set of unique circumstances.
That said, it's important to keep in mind that the Combine is very much split down the middle ideologically when it comes to the change in leadership and the reform roll back. While the bulk of the DCMS is supporting Isokuru—for a variety of reasons not limited to personal loyalty—there is a large portion of the Combine that supports Omi.
At this moment, there is a civil war being fought for the hearts and minds of the Combine's people. Supporting Omi can only help her side "win." Drawing the Combine into a major fight so the opposition can rally around fighting the gaijin only weakens Omi's position by giving the Combine an external enemy to focus on AFTER exhausting what they can get out of Rasalhague.
Remember, Omi's only a traitor if she loses the war for the Combine's soul.
At this point, it's far more dangerous in the long term to keep a guy like Isokuru on the throne—who's really Takashi 2.0—than investing in Omi and receiving the dividends for doing so.
Having the Combine focus in and on itself is far better than having the Combine focus its attentions elsewhere. A domestically troubled Combine is a weak Combine.
As for the Combine's honor, the allies have seen how much that is worth, and really don't trust it at all. (April agreement?) Perhaps the Hegemony might improve relations with the LC, but you really see the Commonwealth and DC improving relations without settling matters on the battlefield at some point? Even Mel, who's going to be a far more mellow leader than Katrina, knows she has to settle matters with this new Combine leader at some point, or he's going to use the "blowing off steam" excuse to pull all kinds of crap.
There's a huge difference when it comes to honoring gaijin and the honor the Combine people bestow and exercise among themselves. At the end of the day does it really matter if Commonwealth-Combine relations or FedSuns-Combine, or even Hegemony-Combine relations improve if the Dragon is too busy fighting itself to fight you? Not really.
Don't want to deal with Isokuru AND the DCMS? Support Omi's rebellion. At the very least, she's a useful proxy to keep Isokuru occupied by allowing him and his supporters to "blow off steam" internally rather than against the LCAF, AFFS or HAF.
IMHO, that's a much better play than going to war with the Dragon at this stage. This is a crucial moment in Combine history, if the Black Dragons manage to burn themselves out in the Combine and Omi regains control of the country, her ascendance offers the unique opportunity to affect real change in Draconis Combine culture and interstellar relations for decades to come. She might be a kid now, but she won't be forever...]