After finally getting to the 2.2 storyline and rereading Yugiri's comments about her homeland, she pretty clearly states what happened and the geopolitical situation that is/was on Othard:
how the Garlean Empire is tearing itself apart due to Emperor Solus finally dying, causing 'the War of Succession' over who would take the throne, given Solus never chose a successor.
The Domans, who were subjugated like all the other nations on Othard, decided to try and take advantage of the political turmoil by rebelling openly against their Imperial oppressors, which tragically backfired, in the Garlean forces counterattacked and literally crushed the rebellion to serve as a warning to the other subject nations. The rebellion wasn't just put down, the Empire literally destroyed the entire nation - Yugiri mentions her small band of refugees are literally all those who survived the rebellion and managed to flee.
So yeah, according to Yugiri's comments Doma wasn't a 'free' nation - it was a vassal of Garlemald like every other nation on Othard, so the information she gives fits with what has long been stated on the Lodestone about Othard being entirely under the Garlean jackboot.