With what you've said I would absolutely do it. I work a desk job and have tried to get into a position to work remotely unsuccessfully for years. But it is a good job and vacation is decent so I am still able to take a good amount of trips a year with the family.
But I've always said to anyone who would listen that I would "travel" (stay somewhere else interesting other than home) three months out of the year if I could. We've "camped" for almost 10 years now and are very used to the lifestyle.
All the usual RV stuff applies so I won't repeat what others probably know more about (what type of rig should I buy, etc). But I will only add/repeat what was alluded to earlier - have at least two ways for you to access internet reliably for your business. It is your lifeline and I wouldn't depend on park wifi. Last I looked at it (should I get the chance to work off-site) I was thinking of a dish type internet setup (like DirecTV I guess) with a 4G mobile data plan for mobile in case the primary failed. That might be overkill, it depends on what kind of link you really need and the type of work you do.
With your kids having a few years left of school I'd take the opportunity. Wish you all the best!