The reason the BD and Corsairs are hostile is the clear link between the Hogosha and corsairs... The hogosha have fingers in a lot of pies in kusari and weild an enourmous amount of influence as a result... The Hogosha/corsair alliance would imply that the corsairs have an impact on the dealings of the government that the Dragons are hostile to.
Therefore, the dragons would fight the corsair influence on the kusari state tooth and nail.
With regards to the OC, the Dragons don't regard themselves as allied, it's just we share common enemies, and don't want to get in each other's ways, plus the indirect alliance through the GC. Dragons don't like cardimine much, but perceive it as a lesser evil than various other things...