Look up the dissolution of Czechoslovakia.

The Czechoslovakia was founded after WW1. After WW2 it become a satellite of the Soviet Union.

After the fall of the soviet regime the Slovak portion started to ask for the dissolution of the federation. They were mostly against the centralization of power in Prague, the capital of the Czech state and of the federation.

The political debate was fierce, but when a decision was taken the separation then went smoothly and was finalized on 31 December 1992.

I'm thinking about something analogous to an "American Civil War style" secession, in which some area which is a part of a larger nation state wishes to politically separate itself.

I know that the USSR breakup was largely non-violent, but I think that was a unique historical event and it's probably not fair to draw too many parallels to other secession movements. I also know that there have been colonies that have peacefully gained independence, but all the examples I know about were very far away from the colonizing power and I suspect the challenges involved in gaining independence were very different than what I'm asking about.