You're right, Gretchen, the President has to act on what he judges to be the best interests of the country without regard to his personal feelings. I'm pretty sure on a personal level, W probably loathes Chirac about as much as the rest of us. But he doesn't have the luxury of acting on it. I think sometimes his face does show it, though.
I think you have summed up the situation pretty well sometimes a President has to do things that they do not like doing for the good of their country.