I think Cain was cut off from anything that usually keeps the military in check. She had no superiors whatsover, let alone civilian ones. And there was no civilian society she and her crew were embedded in or connected to.
So, for all intents and purposes she was the commander-in-chief for a community of people which (as far as she knew) solely consisted of military personnel at this point. Which effectively resulted in Cain assuming a rather totalitarian point of view.
She expected that everybody followed her orders without question and when anyone disagreed with that he or she got quickly eliminated from the community she led.
Summary execution for insubordination during battle can be a proper punishment. Especially considering she could've had a mutiny on her hands if she didn't send a strong message.