Cardassian due process determines the verdict before the trial. It's safe to say she would have been found guilty for something already. The likely problem would be Bajor would not extradite Kira. That would leave the victims with little choice but to settle for what they might consider injustice or do something about it on their own through vigilante justice like what Prin did.
The government was being run by a totalitarian military dictatorship. Maybe he wasn't given much of a choice but to be there. Cardassians occupied Bajor because their own world lacked many natural resources and made up for that by strip mining neighboring worlds like Bajor. Bajor would have been controlled by Cardiassia all of Prin's life where he would have been born into the idea of that world being just another world of theirs.
When I say "due process" I'm not really referring to the Orwellian system the Cardassians have in place.
It might have been interesting if Prin had tried going through legal channels though, even if it ultimately went nowhere. It would certainly come off better than him playing vigilante. I doubt even the Cardassian legal system would condone his actions, provided they were interested in being diplomatic at the time.
Also, we don't really have any evidence that the Cardassian government interferes with the lives of the majority of its citizens, just that when they want to do so, there's essentially nothing stopping them. If Prin was really coerced into being on Bajor, it would be a weakness in the writing of the episode that he never mentioned it.