I've driven all over Boston in a RV -- but it takes a certain willingness to get honked at (a lot) by some of the kinder Bostonian drivers. There are some tricky places because of low bridges and the fact that the propane on board is prohibited in tunnels.
There are alternatives for road trip lodging to RVs and motels. With a family you might find Verbo-style accommodations much easier, the trick is that usually you need to stay at least three days. There are a lot of providers, but typically you would stay in a private home at rates that rival motel rates and you get privacy and an easy way to prepare food.
And for overnight on-the-road stays, you might like the AirB&B options -- Here you rent a room in a house and actually stay with a family. Some of the options ARE REALLY APPEALING over what you can find in a motel in the same places. For instance, look at these prices of places in the Orlando area, etc. You can do other searches by the cities you are considering, but it's possible you can save at least $100-$150 per night over the cost of similar motel lodging this way.