@Mizumachi I gotta say that I disagree with you about the intent of the emperor. He said it himself that illegitimate children are an Emperor's biggest weakness and that he even thought about killing them. Since he couldn't bring himself to do it he instead abandoned them to Ruhahel, knowing how she'd treat them. He ignored the problem : as long as he didn't see them getting mistreated he wasn't feeling guilty, as if it wasn't his responsibility.
Did he want them to die? No, clearly not, otherwise he'd have killed them himself. But did he think naively that everything would be alright? Clearly that's not the case. He knew things would go terribly wrong for them, but he didn't care either way. Turning a blind eye is already being responsible in this case.
So the kids reactions are normal. Even though they are 23 years old mentally, if you abuse a 17 years old highschooler for 5 years straight it's only natural that they'd be distrustful to everyone. Especially towards the father who abandoned them. Remember that they could have died multiple times there : throwing a vase at a 5 years old kid could pretty much kill him.
With this being said, I still agree that this is kind of excessive for two reasons. First, the Emperor is clearly feeling guilty. Sure guilt can't just erase your crimes, and he will have to live with this sin forever. The kids don't have to forgive him and act differently just because he is feeling guilty. Having to endure the victim's distrust and hatred is natural on the road of redemption. Which brings me to the second reason why I agree that this is excessive : this is a work of fiction. This not a real life simulation: there is a plot, and for the plot's purpose the situation got to change one way or another. The kids can't just stay distrustful forever, the story got to move on or otherwise this will quickly get boring. For the Emperor to have his redemption arc, the kids have to somehow open up to him. So I hope they will soon open up and don't stay this way forever, because there are barely no interactions between characters as of now. Whatever the imperial family will do, the kids will always react in the same way, and I can see how this can quickly become a problem in terms of plot.
Also, thanks a lot to the translators for the mass release and the quality translation!