Vader needed something to do, between 3&4.
(round up the wayward systems and "unify" the empire).
--> the remnants of the 'separatist alliance' became the Rebel Alliance. (agreed with r2d2-26)
-===-
which fits with the structure of the trilogy, btw:
ep1) introduce: padme's militarization + qui-gon's defiance
ep2) slippery slope: jar jar takes 'padme militarization' too far; dooku takes 'qui-gon's defiance' too far.
ep3) make anakin choose: he chooses "padme" and loses her, because of slipppery slope -- burns-to-vader ON a slippery slope (just to drive the point home).
--> this forces the Jedi Survivors down the other path: qui-gon's path: to immortality.
(the only thing that separates the Jedi Survivors from the Separatist Alliance, is dooku's "slippery slope". otherwise, these are the same faction).
(it makes sense, that the leftover separatist systems would become disillusioned with dooku, and 'backpedal' from the slippery slope, thus finding themselves on common ground with the Rebel Alliance)