I get where she is coming from, and I agree that the duke should praise him and show the child more affection. And whenever he could, he should be more lenient and spoil him. However, as for his education, I kinda agree with the duke.
I know it's cruel to feed a child poison but this isn't the modern world where she lived as a normal citizen. It's really important for someone in a high standing as Ain to be immune to poison. If he doesn't do it now under the supervision of everyone, he would be made to do it one day under a malicious intention, and perhaps, nobody is there to assist him. The poison should be adjusted that he doesn't become so weak and in so much pain like now though. He could've had died if only it was a little more. Go bit by bit yeah? Do poison in moderation???