RV is totally doable. Or car camping with a couple of tents for privacy. Bike touring works too. Or cruising/liveaboard.
I've refrained from commenting on this thread because i don't have kids of my own, but since people aren't really giving many helpful responses i can share that over the years i have met plenty of long-term traveling families with kids of all ages. The thing is you're not going to be meeting them in a ditch near the hop-out. They're going to be at national parks and paid campsites and marinas and doing the festival circuit, that sort of thing.
Depending on their age it might be good to set up a homeschooling routine so that they don't fall behind, and in some places you might be legally obliged to do that. Several parents i talked with have said that they needed to adjust their traveling schedule and style to accommodate for the kids, giving them time to do their schoolwork, recover from a physical day (especially if bike touring/hiking) and so on.
It might be easiest if you start with a clear target like just the summer holidays, or just a semester on the road, that way it will not seem so daunting for you or the kid. One couple i know started with a year-long tour of the national parks and now it's a couple years later they're still traveling i think, so you never know. I imagine a lot comes down to how comfortable you are being a parent and a teacher in one, and how independent the kid is, how much they want to hang out with other kids, that sort of thing.
Just to reiterate, though, i am not a parent, do not have kids of my own or any exposure to kids in my extended family, so i am only relaying what i heard from parents i met in campsites, at festivals etc. I know there are a few people on StP who have traveled with their kids in the past, but not sure if they are still around. I'm sure if you get out there you'll meet people, though, especially if you go to more family-friendly places.