Why would Rheinland ever want an alliance with Corsairs? Why would the Corsairs want one with Rheinland? If an alliance deal came through, it would probably consist of Corsairs abandoning their robberies in Sigma-13, why would the bloodthirsty pirate nation ever want to do that?:P
Aside from that while Chico has a good point, and there would likely be opposition against helping Rheinland fight off Liberty amongst the Hessians (there may be one among the Bundschuh), the motion that the RHA is going to follow will be to help the Military hold off Liberty for as long as possible in order to drag the fight on and drain both the Rheinland Military and the Liberty Navy of their resources. They don't need to attack the Rheinland Military to do that, since it is already quite a lot weaker than the LN (in RP). If the Hessians succeed into driving the war into a stalemate (even if with Liberty having a slight advantage due to their war fleet), the Rheinland Revolutionaries would likely be able to garner more support at home with the far weaker Military and Police presence. Rather than giving away Hamburg and New Berlin to Liberty in return for having their own small one-system province, they would be able to unite Rheinland under one banner and replace the government in one go. And the spiel goes from there.
So basically the stakes are much higher here. Remember that Rheinland unlawfuls have a strong sense of nationalism and comradeship. They won't be fighting each other when the future of the entire house is possibly in their hands.
Not to mention while the RM is busy with the LN up north, it frees up more resources for the Hessians to throw at Omega-5, 47 and 11, which also benefits the SCRA...:P