Holy cow, 2 weeks and you don't have reservations already?
Where to stay: With a popup, you have a little more flexibility, as long as you can do without hookups. Nevertheless, at least half of the campgrounds inside Yellowstone take reservations (through Xanterra.com) and are likely to be full. The first-come, first-served campgrounds (check Xanterra for the list) will probably be full by midday. You can stay outside the park - there are some nice national forest/national park campgrounds (no hookups) in the Tetons if you're coming in from the south. If you're coming in from the east (Cody), be aware that Cody itself is a good 2-hour drive (one way) from the Yellowstone Grand Loop road (which is where you need to be). Plan on a minimum of 3 full days in Yellowstone to just skim the highlights; 4 or 5 days better, especially if you want to include the (next-door) Grand Teton National Park. (One entry fee of $25 per vehicle covers both parks for a week. Keep your receipt.) Most convenient place to stay outside the park or if you need hookups is in West Yellowstone, which is, as it sounds, on the west side of the park. Grizzly RV, two different KOAs, some smaller private campgrounds, and Henrys Lake State Park (Idaho) are decent choices. Call ahead NOW to reserve a site. I strongly recommend you check rvparkreviews.com for information on CGs, and do a search for "Yellowstone" on this site for "what to expect."
Briefly, what to expect - lots of driving, 45 mph or less, beautiful scenery (much milder & less spectacular than Colorado), high altitude (most of the park is 7500 feet or higher), lots of wildlife (especially bison), some of which will be right alongside the road or even on it, none of which is tame. Thermal features (geysers, hot springs, etc.) in many areas of the park, but concentrated in a few areas. Also expect lots of fellow tourists everywhere.
Supplies: bring clothes for layering; bring rain gear - the park has been wet this year & is often cool at night. Cameras & binoculars for sure. Re: food - there are restaurants (pricey), hot dog-burger-ice cream places (not all that cheap) and cafeterias in the park at the major lodging areas (Old Faithful, Canyon, Lake, Mammoth, Grant Village). Yellowstone General Stores often have small grocery stores (very pricey). West Yellowstone has a couple (pricey) small grocery stores. Cody has a Walmart.
What to do: Sightsee. Depending on your family's interests, there are some activities offered in & around the park, such as horseback riding, scenic boat tours, fishing (Wyoming licenses required, but short-term ones are not terribly expensive), hiking. Be sure to check with the rangers before you hike, as there are some restrictions and some very important cautions you will need to know about. There are also other activities outside the park - the Cody rodeo, a brand-new rope climbing/zipline park in West Yellowstone, the Grizzly & Wolf Discovery Center in West Yellowstone - lots more. Swimming, TV and Wifi connections are rather limited in the area.
2020 Toyota Tundra CrewMax 5.7L V8 w/ tow pkg, Equal-i-zer
2020 Lance 2375