The problem with this situation is he's not coming from a place of genuine care for this girl. He's just annoyed she's costing him money. And both his wife and this girl are likely to sense that and team up against him if he starts pushing harder. Which is not going to be a good thing for his marriage. His marriage, the most important thing here.
If he can't convince his wife to get on board with steps that might be better for her daughter then he needs to just learn to either accept it or divorce her over it. A pissed off middle ground, constantly trying to save money by evicting her while uttering the lie he's only doing it because it's good for her probably won't do him much good.