RV experience vs. saving money
Some people enjoy renting RVs as it's a different way to travel and it's all about the experience. In that case, there's no reason for you to not rent an RV if that's what you want to do. However, if you're doing it to save money on your trip, it's not the right choice for you. RV travel, especially when you also have to pay the rental fee, is never the cheapest option.
This article gives you helpful tips on how to decide betwen an RV or hotels. Here's another good article with helpful tips. The last article does say that studies show RV travel is the cheapest way to travel. I believe that might be for those who already own their RVs. RV rental fees for the week can easily cost as much, or even more, than hotels would.
Anyway, we used to be avid RVers taking our kids camping in a truck/camper combo and then, when they were bigger and we needed more room, a truck/trailer. However, we never did this for long trips as the gas consumption was pretty high and long miles negated any cost savings we had by hauling our sleeping quarters and kitchen with us. Whenever we went on longer trips, we did the car/hotel thing. Depending on the trip, we sometimes took a tent and camped at least some nights along the way. Now, with the kids gone, we still take the tent and will often tent camp for the night, mixing it up with hotels depending on our destination and other factors.
An RV wouldn't mix well with DC but there are RV parks outside the city that have transportation to get you to the Metro so you can explore the city. Hotels in DC tend to be quite expensive so this might be an area where you would save some money. However, you could also stay in a hotel well outside the city and park you car at the park-n-ride lot for the day so you can take the Metro into the city. I wonder if some hotels might even have shuttles to take you to the Metro stop? It might be worth looking into. Personally, I wouldn't drive in DC just due to parking issues in the city. And the Metro is easy to take and actually a lot of fun!
I suggest you read the articles and see what you think after that. And keep asking questions.
And do you have any questions about where to go and what to do?