For what it is worth, IMHO most kids are better off in a normal school (public or private) situation. All though my DW and I are both retired teachers, we don't feel that we would have wanted to home school our own two children. With an RV, keep the kids in school, but use vacation time to take them to as many places as you can and the experiences will will teach them that there is a lot more out there than what they experience in their hometown.
Or, as an alternative, and if you are really qualified to provide home schooling, take 1/2 of a school year and a summer for an extensive trip. Prior to leaving, try to get as much information about the curriculum and courses that your child will be missing and make sure that you are capable of teaching that material.
I'm not saying that it's impossible to go full time and educate your child, but I think it is a lot more difficult to do it well than most people expect. And yes, traveling and seeing the country makes for one heck of an education. I was a military brat, and in the course of my childhood, I attended 12 different schools and spent time in Virginia, Hawaii, New York and Maryland. I learned a lot, but a lot of kids in military families have problems with the transient life. I've only learned in recent years how difficult it was for my older sister and how it contributed to a lot of her insecurities.
Whatever you decide to do, good luck and enjoy your RV travels.