I don't think Perpetua is the Demon Queen or related to her.
When meeting the Black Knight, Perpetua was like a fan girl who see her for the first time.
But the theory is cool :)
I think Perpetua will have the potential to become the next Demon Queen. Maybe the Demon Queen will leave her position if she lost a battle against MC and Perpetua come at the right time (like when you choose to willingly sacrifices yourself to Amy and Perpetua was "It was my plan all along you fool").
"Mwahahaha ! Demon Queen, you fell into my trap and lost against my minion/rival. The throne is now mine !"
I hope there will be lots of twists with Perpetua ;)
Vivian might be a good hidden boss to play the Demon Queen, but it would be too obvious as the proprietor of the brothel playing matchmaker.