Yeah, I'm really not convinced the prince and sister are behind the assassins.
Now don't get me wrong, princey seems like a dumbass and the sister is at best really not considerate of her sister's perspective, but we've got zero evidence that they sent the assassins, only Karina's assumption. Given how we already know she's a pretty distrustful and scheming person, a fair bit more villainess-like than typical villainess heroes, I feel that's coloring her perception a bit.
Sending assassins to kill off your sister after exiling her might make perfect sense as a plan to Karina, but the prince seems too straightforward to think of that (given the usual stupid move of breaking off the engagement in the middle of a ball), and Aurora... Well, we've barely seen Karina and Aurora interact, so I'll hold off on judging her for now, but going off the one time with the dog plush she really just doesn't seem like the type of person willing to kill her sister, especially since the family seems to have kept her out of noble politicking due to her health. It's also notable that it's always other people that are asking Karina to give up things or take on responsibilities for Aurora, not Aurora herself.
Now, I could be entirely wrong, the prince and the sister really are out to get her, and it's just that straightforward. But I've got a gut feeling there's gonna be a twist.