It’s a common trope in sci-fi that Earth has a World Government and similarly the Aliens have only one government as well.
But in historical First Contact scenarios like the discovery of the New World the fact that the groups involved were not unified played a major role - think Cortes using the other groups to overthrow the Aztecs, or the various alliances that North American tribes had with different European powers.
Are there any books that deal with this scenario? Like I imagine that if First Contact happened at the height of the Cold War, there would be incredible fear about the other side being able to leverage the aliens for an advantage.
It sounds like Three Body Problem is right up your alley!
One of the basic premises is what happens in First Contact when Earth fails to unite.
Not directly related, but you might be interested by Family tree by Sheree S Tepper. The aliens aren’t actually. Kinda.
Star Trek has a bit of that here and there. Klingons are basically at a constant state of cold war between different clans and the Romulans are actually Vulcans that have split off from the Vulcans after a civil war. And of course there is a lot of political infighting within the Romulan Empire as well.
While this might not fit 100% but I really liked The Moon Is a Harsh Mistress by Robert A. Heinlein in which he describes a conflict (thats one of two main plots) between unified Earth and the Moon which is a giant penal colony.
