Really the Dragoons only despised working for the Free Worlds Leauge and the Draconis Combine. This is because the FWL was in a situation where the dragoons almost had to fight each other. The combine tried to force the Dragoons to join the DCMS. They also Despised Old Comstar (by extension the WOB) because their Stanglehold on Technology and Communications was so contrary to Clan Space.

In all honesty, the Dragoons in their Prime were capable of beating back any houses Military for a good long time. While not the largest, the Quality of Pilots in their Military are considered the best of th best. Unless a house was willing to commit at least 12 Elite Regiments to attack the dragoons, they were a force to be reckoned with on their own