Also, the fact that Earth is but one of many planets, it is natural to assume that Earth's will (or Vulcan's, Andorian's, other founding members', etc.) isn't absolute. Couldn't factions be formed within the federation where some planets who identify more with a certain point of view that isn't aligned with the mainstream Federation "official" line, gravitate towards one another?
Maybe. Or maybe it would just lead to the formation of political parties and to competitive elections.
And couldn't these factions lead to divisions within the Federation, leading to unrest and possibly all out civil war? I think it could.
I think you're projecting modern political culture onto the Federation and its Members.
One of the important things to remember about the Federation is that it and its Members have internalized the idea in their mainstream political cultures that violence is the absolute last resort, not an acceptable means for resolving domestic political disputes. They are committed to democratic governance.
Further, it seems probable to me that if the Federation ever finds itself with a truly insurmountable cultural difference with one of its Members, that it is far more likely to simply allow that Member to peacefully secede if it holds a popular referendum that decides in secession's favor.