In that case, the half that's "wrong" loses their gun privileges and gets a dishonorable discharge. Inciting a coup against a democratic republic is like threatening the local impound with a gun when they won't give you your car back. You're avoiding the agreed-upon process, and escalating the situation so far that you will never be taken seriously even if your ideas are agreeable or good. State rhetoric will always outweigh cults of personality and arguably even the free press.

Modern militaries can't really be divided, since in order to operate they needs huge amounts of money, fuel, logistic support. If a unit goes rogue their comms would be shutdown and their supplies would run out.