Okay so let me get my thoughts straight.
I think the prince doesn't really love psyche. He prolly considers her as a tool for some purpose we don't know yet. And as seen in a previous chapter, where he got annoyed when he caught psyche reading a complicated book, and in this one, he wants her to remain naive and simple-minded to the point of imprisoning her so she wouldn't get involved with medea.
And for medea, the reason why "she wants to be her, just for a day" is neither because she's jealous of psyche, nor does she want the prince's affections. She simply wants to be queen. But her reason why she wants to rule might not be so simple.
Gosh I WANT MORE.