Couple of comments from a family that homeschooled two kids from pre-school through high school - both National Merit Scholarship winners and now in top-tier colleges. It can be done but it takes a LOT of effort from the parents: curricula planning, standardized testing, tutoring sessions for advanced work, cyber-classes through Stanford EPGY, etc. There is an excellent resource on the internet for you: www.welltrainedmind.com - look for the link to the forums. Participate in the forums as there is a TON of wisdom there for you (just like RV.NET).
We were fortunate - there are about 800 homeschooled kids in our community with AMPLE opportunities for talent shows, debate teams, special-interest classes, tours, basketball/baseball, speech, choir, handbells, and many other group activities with some of the nicest kids you could hope to meet. That will be a challenge in Road Schooling. If you go to a place and stay a while, look up the local homeschooling organizations and participate in some of the activities! Each State has a state home school association and many communities have a local one.
Good luck! What a marvelous opportunity for your children - but what a huge effort for you if you really want to do it well!