My read has always been that Théoden was still unsure about what to do with Grima after what has been revealed. He is clearly angry at him, but it is also difficult for him to let him go, after he had has been his closest council for so long. When they meet Saruman and Grima at Isengard, Théoden even tries to plead with Grima again. And it doesn't make sense that Théoden is trying to lure Grima, because if he is trying to be cunning, he would well know that Grima would never bother, instead, it reads as Théoden still holding out hope.
So yes, it is questionable to send Grima away. And Tolkien isn't exactly subtle about it.