I would say the head of the Patrick family is very level headed. Very just.
BUT
He should not made that decision known with Ian so much weaker than Jurion. Either execute or shatter Jurion's core, and side with Kayden and Gestella so that Ian is protected and has the opportunity to learn with outside forces.
Taesung should not be seeking evidence, he should be stabbing the old man during dinner!
No matter how guilty he feels, there is no reason to leave the villain alive, and he could arrange easily to not be blamed himself for it.