Good question. The Nabokovs' first trip west, by car (a Pontiac, driven by Dorothy Leuthold), was in the summer of 1941 -- before rationing was imposed following Pearl Harbor. For the remaining war years, the family traveled west only once -- by train, to stay at J. Laughlin's Alta resort in Utah. (They were semi-marooned all summer high in Little Cottonwood Canyon, since they did not have a car at their disposal, nor did they know how to drive.) They spent other war-years summers in the northeast.
In '47 they had a grand vacation in and near Estes Park, CO -- but got there by train. It was only in '48 that they acquired their first car, and in '49 they took their first driving trip out west (Vera had learned how to drive but even so she shared behind-the-wheel duties with Richard Buxbaum, an agreeable Cornell student who was a companion for 15 year-old Dmitri).
I've been reading the free intro on my Kindle, trying to decide
whether or not to purchase it. A question: How did the Nabokovs
deal with wartime rationing of tires and gasoline on those
cross-country trips?