I honestly don't know what he expected would happen, maybe he was just that desperate. I'm quite surprised she told him of the poison before he made his sister drink it. I thought she would go "Hahahahaha, how does it feel, to kill your own sister with your own hand! Don't worry though, I'm sure your sister can no longer feel any pain now, haha...HAHAHAHAHA." Like that.
What I don't really understand is why he show such despair, maybe I would understand if he made his sister drink that poison or actually kill the maid to get potion for his sister and to find out it was for nothing. But he let the maid go, and his sister is still sick but alive. Basically, he just got back to square one...wait not even square one, it is likely that if he wasn't the one to do it, some other person would've killed her under her order, too afraid to defy her. Meaning he actually saved one life, doesn't get himself or his sister killed for his attempt at outwitting her(surprisingly) and an additional free bottle of poison that he likely used to kill her.
Though I guess that's because unlike him, I have zero expectation she would actually heal my sister properly and wouldn't bother to ask in the first place