@Nep Uh no, it'll just teach his daughter to be another naive pure hearted brat that will get involved to troubles. He has to teach her not only how to care about others, but also about apathy. This is a cruel world, where unnecessary sympathy could get you trouble, and right now when the MC planned to separate from her, it is even more important to make her learn about apathy, it's to protect her from jumping into troubles.
And for your point: 1) who the fuck care about the girl's trust issue, she's a stranger, don't unnecessarily get involved with stranger, especially a troublesome one, he should teach his daughter this if he planned to separate from her later. 2) sure he doesn't want it, but it's not a problem either, and it'll make the girl go away quickly, stay away from problematic individual. 3) what problem are you talking about? if he take the money then it's a done matter, not taking it however, would just get him more involved with the problem source, that it the girl.
And no, the MC is not a hero, he's the hero's mentor. If it's a hero nature that is sympathy and get involved, the he should teach him apathy and stay away from unnecessary problem.