The Golden Chrysanthemum are dedicated to similar ideals as the Blood Dragons, but basically they want the same basic rights that all men in Kusari enjoy, both in the workplace and at home, being allowed to pursue careers in any field etc.
They also want to completely sweep away the existing political structure of Kusari and effectively install what Bretonia has: a ruling female queen (Empress in Kusari's case), with a democratic style parliament, women being allowed to vote etc. It is because of this that the GC strongly support and assist Bretonia in the war and hope for a favourable Bretonian outcome. Either Bretonia wins, in which case the GC feel they'd rather be under the leadership of Bretonia and a Queen who would guarantee them freedom and equal rights for definite, or else Bretonia wins and it weakens the current Kusari regime to the point where GC and BD can topple it and install their own regime. Either outcome is suitable to the GC (they are seriously radical and fanatical after all, whereas the Blood Dragons are somewhat more conservative in their goals).
The Golden Chrysanthemum absolutely hate Samura, because it effectively rules Kusari through its many political puppets and as such it maintains the male dominated stranglehold on Kusari society. It is unlikely that the Golden Chrysanthemum will ever stop fighting while Samura has any kind of power within Kusari. It was Samura agents, abetted by the Shogunate of the time, that killed the founder of the Golden Chrysanthemum movement, after all.
This is gathered from infocards and my own RP take on the whole background situation, so I hope it helps/makes sense.