Probably using her authority as the most foremost executioner, using evidence that the princess was rejecting her requests and reasoning to say that killing the princess is worth it. You must've seen how
loyal that kid was to her after all. "I saw it in a dream" is just a factor that's making her determined towards killing the princess.
Didn't expect the author to include the dramatic increase in executions that followed the invention of the guillotine in this story. Seriously, look at how many people were beheaded in France during the French Revolution. There was a period of time where they just had day-long events of feeding processions of people into them.
The Terrors of Robespierre are really NOT something you want to use as a comparison for that. They were executing everyone and everything that stood between them and utopia... and you can't exactly murder your way to utopia.