The reasons why she was pushing the prince to be with the bitch were kinda obvious, a few chapters before i think it showed what could "Possibly" happen with the prince not to mention explaining why he is like that (super intelligent and stuff), it was just a matter of connecting a few dots here and there.
What the MC does not realize its that she can perfectly achieve that perfect ending she wants for him by being with him, but maybe all of this its just necessary to make sure the prince completely falls in love with Bertia rather than lose interest in her before it happens, because i believe the one thing he can't get a complete read of their actions its her.
This is just an extra long courting dance people and we are about to reach the end!