Of course we have no idea why the Separatist worlds want to separate in the first place, due to poor writing by Lucas. Given that, one would assume that if any world or nation wanted to divorce itself from it's "motherland," it would just sort of declare it and then defend it's own land. For instance, if Texas wanted to be it's own country, it would simply say it and then expect that the military of the United States would come across it's borders in order to take control back. We see that happening in the former Soviet republics.
Which leads us to Kashyyk. Why on earth would the Separatists fly across the galaxy to attack another planet? What's in it for them? Like I said, we know practically nothing about their discontent or their overall cause, but if it was because they were simply not happy being part of the Republic, then wouldn't they just concentrate their energy on defending their own worlds? Why expend resources to attack another sovereign world?
Naturally, George just wanted to shoehorn a Wookie battle into ROTS somewhere to make up for not having them in ROTJ, but is there an actual story reason for this invasion?