They didn't exile her to the monastery though. Before she could be charged, her dad sent her there to protect her from having anything else happen to her (because she'd likely be punished worse). She wasn't even there long (like a month) before Michael came to break her out. It's likely they planned for her to be there while things cooled down. That's why everyone looked at her dad funny because he didn't tell her that it was a part of a plan he came up with.
As for the (ex) crown prince, he volunteered to step down from his title and status to atone. He realized he didn't have what it takes to lead. The saint mainly harmed herself, so they probably took that into account.
But as an heir apparent, that level of incompetence is a crime on its own. No investigation, no corroborating evidence for the decision he made. Crazy exile was his only punishment because it might mean he did his other duties with a similar level of negligence.
And a fake saintess, doesn't that undermine the authority of the temple. She was their representative only to deceive and commit crime (used or not) and her only punishment is house arrest and repentance (she chose to leave). That's it. (╯°Д °)╯╧╧
Exile them to a harsh monestary, the same as they did to the MC