I believe that you are talking about what happens in Chapter 19. You can find more details about this answer at the very start of that chapter.
In that chapter, the Wakatsuki family is about to leave the camp at Manzanar. Jeanne says that Papa decided that if they were going to leave they were going "leave in style" and do it on their own. Mama wanted them to take the bus, but Papa would not listen.
To me, what's going on here is that Papa had not been able to be "his own man" for all these years. So now that they were able to leave, he wanted to take control and do it his way -- that's why he bought a car rather than using the bus.