That's another point, it was supposedly only the UK and America that revealed their sleeper ship construction point to the Coalition. Not really sure how they were supposed to have found that out, but that's what they said. Neither Bretonia or Liberty officially checked their evidence either, although some of their people seemed rather keen to do so and perhaps make up for it to prevent conquering (the term "apologists" fits well here).
Whether that is true or not, they need to conquer territory for more resources, and if the war were to continue working in their favour they'd likely keep going until they ruled all of Sirius.
If you did get all of the houses unified, then you could do whatever you wanted with Gallia to be honest - that's a lot of military strength to back up any demands. However, it's never going to happen for ooRP reasons of stopping all the wars and making things fairly boring (plus the RP reasons I mentioned), and if it really were I think it'd likely be some great common need instead of some Sol-throwbacks asking them nicely. Everyone can dream though.