We did a driving trip among the western national parks some years ago, and we started with the idea of renting an RV -- we mistakenly thought it'd be cheaper and more convenient. After crunching some numbers, we realized hotels were considerably cheaper.
I just checked a few numbers to see if that's still true -- I didn't put much effort into it, but here's what I found online with a few minutes of checking -- I assumed September 1-8:
Renting from Cruise America: Unfortunately, the website won't give me a price for the "standard" RV, but the large RV is $1190 + $245 for an estimated 700 miles (could be more if you exceed the 700 miles). Renting the RV also requires a $500 deposit, and you'll have to pay for gas, which won't be cheap. Presumably, a smaller RV would be cheaper.
In contrast, cabins are available inside Yellowstone. They have lots of options, but I first picked the Lake Lodge Cabins -- no reason; I just liked the name. They offer three levels of cabin in this area. Pioneer cabins are very basic with just beds and a private bath, and they're $90/night. Frontier cabins are larger, and they're $140/night. Western cabins are recently remodeled, and they're $209/night. These cabins include no kitchen, but a cafeteria is available in the area.
Next I looked next at the Lake Yellowstone Hotel, and they have rooms varying from about $162 - $711/night. So some of these rooms are quite expensive!
What I did not find is a cabin with a kitchenette, but I also didn't look thoroughly.
I've stayed in cabins at Yellowstone, and while they're nothing special, they're clean and comfortable -- and would be much more comfortable than a tent with a small child. In another spot, these wouldn't be a good value, but in the jewel of America's national parks, you're paying for location.
The town of West Yellowstone (located, I'm sure you'll guess, outside the western gate) has some chain hotels that might be a good deal too. We enjoyed the Wolf and Grizzly Discovery Center in West Yellowstone, and I remember they had a really great pancake place with an Indian-type name. If you were to stay in West Yellowstone you'd have access to non-park prices for food.
Other thoughts:
- They sell gas inside the park, but you don't want to pay their prices; be sure your vehicle is full when you enter the park.
- Every area of Yellowstone has its own museum, a restaurant and/or cafeteria and/or a lunch counter. Sometimes the lunch counters are located at the back of the gift shop, but they were a better bargain than the others.
- The park is bigger than you expect, and traffic can be awful.
- Note that when you pay for entrance to Yellowstone, your "ticket" is good for a week's entrance to BOTH Yellowstone AND adjacent Grand Tetons National Park. While Yellowstone has a larger variety of landscapes, I found Grand Tetons to be more beautiful. The single best hike was at Jenny Lake in Grand Tetons.