I mean, thinking about it reasonably, the prince has all the reasons why to kill the Kueen. He's not only not her flesh and blood, she's active, charismatic and strong, with a decent amount of influence from what we can see. Even if he's the heir to the throne, she'd likely sideline him so hard he wouldn't become king until he's late in his years, if he doesn't die before her.
Not saying he's justified (she's letting him live freely, if he has enough freedom to hatch a plan to kill her that becomes successful), but that there's understandable reasons to do so.
Do wonder what kind of horrible death he'll die for his transgression against a mother tho.