Camping doesn't come down to just $. It's a lifestyle choice and for some (us) a sleeping in your own bed issue. If you add up the cost of the RV, gas, insurance, road side assistance it's probably more $ then a cheap hotel. Once the RV is paid off you come out cheaper. For a family of 7 it may come out cheaper with an RV.
As for rental, I think most RV owners would not rent out their personal RV. Someone being in their space, higher insurance, breakage, wear and tear. I have also heard of people leaving the black tank open and it filled and got hard and had to be replaced. The phrase "party bus" also comes to mind.
I could have written this answer myself. I agree with everything said 100%.
Hobbies and leisure activities are not really about making financial sense, but more about quality of life. If an RV is something you would use a lot and make great family memories, it's worth it.
I doubt you would find a motorhome that sleeps 7 comfortably, but a bunkhouse travel trailer would be a better option for a family that size. A large passenger van would accommodate 7 and pull a travel trailer. We own (but don't use for camping, our son lives in it on our property) a Keystone Cougar. It has a master bedroom in the front with a queen sized bed and the back bedroom is a bunk room with 4 bunks. While the dinette makes into a bed, it's rather short. The couch pulls out into a large bed, and is much easier. That could sleep the 7th person, or two kids could share the double bottom bunk in the rear bedroom.
There is NO WAY I would rent out any of our personal campers. Ever. Nope. I think once you own one, you will realize you don't want to do so either. I suppose if you are buying RVs for rental only, and not going to use them for your family, it would be different. But, once you have one that is clean and has all your stuff in it for your family, you're not going to want other people messing with it.
All that being said, I also agree with the post about trying a pop up. The one we currently own (our 4th) can sleep 7 people. We have actually stayed a week at the beach with 7 of us in it, 3 adults and 4 children. On the king sized bunk, we use hanging fabric shelves (5 sets) lined up to separate it into 2 private twin bed sized spaces when there are that many people with us. It's a small space, and not a place you would want to live permanently with that many people, but we live outside much of the time, other than sleeping. We also set up an instant tent, that is large enough to stand up in, to keep all the clothing and act as a changing room. We only do this when grown kids and grandchildren are with us. We do have a full bathroom w/shower where we can change when there are just a few of us. We paid either $1,200 or $1,500 for this particular camper. I don't remember which, as we've had it around six years. We can tow it with our mini-van, which is a huge plus to get 20+ mpg over our truck which only gets about 12 mpg.
We have 5 grown children and tent camped our entire lives. We only bought our 1st pop up when our two youngest were teens. We love camping and go often so having a camper makes sense for us. We paid cash for the Keystone about 4 years ago, I think around $11k, but after a couple of trips realized that it didn't fit our camping style. We were going to sell it, but then decided it was a good fit for one of our sons, as he suffered a TBI in 2013, so needs to live close, but gives him his independence as well. So we set it up on our land for him.
As far as camping at the Fort, you can always set up a tent on your site as well. I love that we can have up to ten per site, and we often have some of our kids' families come and go different days while we are there. They can set up a tent on our site for their own personal space. If you have teens, this is a good option as well.