Having made this sort of move several times in my youth with my parents, and a couple times as an adult, stick to the interstate as the others have said. Don’t worry about the mountains unless you’re doing it in winter, the moving van will be able to handle it if it has been properly maintained. 99% of the gas stations next to the interstate will be able to accommodate your situation, as well. If you can, break it into 3 days of driving 6 hours or so. Figure each stop will be about 30 minutes long with any food stops being up to an hour.
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