Cass definitely wants to be Queen. I can see her wanting a child to solidify her legacy as monarchs, as well. Not to mention, to piss off her dead father who shunned her - she would join her bloodline with MC's, and produce an heir that Regis would hate.
She absolutely doesn't want to be queen. She's fine with Mc being the actual ruler and her doing things on the concil behind the scenes. She has literally nothing to gain from having a child with the mc and literally told the mc that she doesn't want him to get her pregnant and is probably someting the mc is going to ave to try to convince of down te line. And why would she care about making a dead man angry? He's dead. In her eyes she already won when the coup was a success and he's pretty much a vegetable now.
Unless I've got things very confused, the King isn't dead, he's "sick" since he was poisoned.
They treat him as dead because there is no cure yet.
There could be a major twist, since they've found a cure (not perfect and with a low success rate)...
If he recovers, enough to talk...
At least Cass was smart enough to say more than once that "she" didn't do anything, since it was Priscilla...