Stay neutral. We only have to lose if we get involved in this war. However, a denial to either sides would also sound bad and would have a bad psychological impact over the diplomats and our relations. So, offer them humanitarian aid... to both parties and defend our assets in Omega-7 if anyone decides they represent a good tactical position.
As for the hessians, no... just no. They're hiding fugitives and thieves. They represent nothing more than a bunch of criminals. What political support? They're brainless murderers, not some liberation army like they call themselves.
Now, the third option is interesting. You think you can handle such negotiations? If yes, why haven't you, the Guildmasters, start such negotiations when the Bretonia - Kusari war started? Or when the Liberty - Rheinland started, eh? I say we'd better stay out, completely.
To sum it up:
Military support for: Neither
Political support for the Red Hessian cause: No
Attempt at brokering a ceasefire and diplomatic resolve of the conflict: No