Part of what makes things a bit hard to follow in SW is that Lucas has, uh... roughly zero grasp of socio-economic reality. This is where his left-wing attitudes shine through the most. His idea for the Clone Wars was essentially: "like the US Civil War, but instead of slavers seceding, it's evil corporations... and instead of Lincoln, you have Hitler pretending to be Lincoln".
And this makes no sense.
Everything tells us that the corporations already control the Republic, and just as the megacorps have the centre of their power in the urbanised regions in the actual world, the galactic megacorps are centred in the Core. A realistic CIS would be a movement opposing exploitation by the Core, and thus opposing the megacorps.
Dooku, an aristocrat, does make sense as a leader for them. That does track with the actual essence of the US Civil War: capitalist-industrial urbanism versus aristocratic-agrarian ruralism. Lucas didn't grasp that context, and just went for "Republicans bad, capitalism just like slavery, hurr durr". But realistically, the CIS should be socially reactionary, anti-corporate, and dedicated to "Systems' Rights", while ideologically advocating for traditional forms of governance (e.g. aristocracy) as opposed to "democracies that are just bought by the plutocrats".
Consider it like this: if the Core is the economic heart of the galaxy, and most people live there, then even a successful secession is bad for supposed CIS megacorps. At best, their biggest market is now behind a tariff wall. At worst, they face an embargo. But now suppose a more realistic idea: that the over-populated Core relies on the Rim for food and for raw materials? And then the Rim secedes! The Core would then oppose secession because it means their economic ruination-- if not outright starvation! So of course they vote for Adolf Abraham Palpatine, who promises that the "galactic union will never be torn asunder!"
That makes sense.