It won't be easy, IMO. It would be a welcome feature if there were a flexible rotation input inside the shader. Problem is you can't add (rotated by transform shader) vortexed cloud through blue shader 'add' or via child input on a surface shader, because the original cloud will stay in as well, you can't mix (blue node; mix scalar) for the same reason, but you could try using a mix controller like a soft simple shape in the same location to cancel out the cloud in that area and mix in only the vortexed cloud. Theoretically, never tried it. Problem is then that the simple shape needs to be rotated as well. For each vortex! So you end up with a lot of nodes. And usually a vortex cloud will be pulled by another vortex if it's close enough, so this method (if it works) won't be natural.
Like I said, not easy.