Thanks for all the thorough points everyone. I really appreciate the advice. Responding to a few questions:
@todedtoes, my wife feels OK with driving out with kids. She will likely bring a friend or her mother to help out while she drives. She'll probably stop a bit along the way. The hope is that we'll get an RV in good enough shape that breaking down is unlikely. I appreciate your concern though.
The whole reason we wanted to take an RV was to be able to see all these places, but have a better travel experience for the kids. They'll much more enjoy playing games and eating at a table rather than being strapped into their seats in a minivan for a month.
We're also able to pay cash for the RV if needed, so a loan is not an issue.
@Matt_Colie, as a fellow engineer, of course I have a spreadsheet! Several! Here's one that calculates the one-year cost for several years: https://docs.google.com/spreadsheets/d/1wmKZeY1EWC7Q5uUiy3RntuztcQIUWNudRpVBOX9hIO0/edit?usp=sharing
@theoldwizard1, I'm not sure how much we'll use it after the big trip. We plan to take it on a least a few test runs before that. My spreadsheet above includes the number of equivalent rental days to break even.
Based on the numbers, I think we're leaning more towards renting right now, but please let me know if my numbers in the spreadsheet are way off.