Maybe they didn't punish them as it will effect the reputation of the Imperial Family. Though, that's most unlikely so, perhaps they'd use it as blackmail for the future? We didn't see the thoughts of Aileen's reasoning as to why she decided to not take it to court. It would be nice if they had included as to why.
If they had their crimes released to the public, the favor for King Claude might increase. But then again, it could also decrease as the other opposing party might say otherwise, spread their shit around, and can get messy from there. It wouldn't be good, especially in an important opportunity and time of making him Crown Prince. They should crown him as they did, and then raise King Claude's reputation to the public favorably first, I think. If they reveal their crimes now, the process on both matters would be much difficult.
As for the attempted sexual assault, King Claude wouldn't have turned into a dragon if they didn't anger him. Having Aileen get beaten up, surely, would suffice. But they also had the plan of making her as the bastard's second wife hence, they decided to kill two birds in one stone. That also made the bitch pull out the sword, and that lead to Aileen getting it by rash measures. Subjects about sexual assault are indeed sensitive topics, just as murder is, but I don't think it's an unnecessary detail. But maybe there is another way that I haven't stupidly thought of.
If the damsel-in-distress trope is the problem, and I think it's obvious, King Claude didn't save Aileen like a prince in a horse solely alone. He gave her the reassurance and will to fight by appearing, and took the bastards off guard by his being there and turning into a dragon. Aileen did the rest as what I can see.
But that's my interpretation. I could be wrong. Hm...
I love her lines "You're not the protagonist, I am." Yessss
