Personally, I think taking a 40-day trip with 2 children and staying on parking lots would get old real fast.
Why don't you plan to stay in a RV park every 4 days and relax in quieter, more pleasant surroundings. You can dump and flush your tanks good and load up on fresh water for your tank. You can do a general cleanup of the inside, take longer showers, replenish your groceries, perhaps let the kids swim in a pool and you could sit under a shade tree with your favorite beverage. This sounds like a better vacation.