We had a family reunion in Yellowstone 2 years ago. Half of us took our travel trailers and the other half stayed at Canyon in their cabins. Each group had good experiences.
My sister's family liked Canyon. It was comfortable and quiet and the dining area was pretty decent.We liked staying in our camper because we felt like we got a closer taste of the natural surroudings. 'Course, that might be due to the buffalo that walked through our campsite and peed behind the trailer.

The good thing about taking a trailer is you can drop it at the campground and drive your car around. NO WAY would I go over the Dunraven Pass in a motorhome
If you know your dates already you just need to figure out whether you want to stay on-site or off-site. We spend a few nights in West Yellowstone which we found very convienent to the west and south sides of the park. Yellowstone is huge, the size of Rhode Island. Forget just driving around and seeing everything. We stayed there 10 days an *still* didn't get to see everything. Get your reservations as early as you can so you can get what you want.
Once you've decided on your hotel, might I suggest you plan to take the kids on the Roosevelt Chuckwagon. It's a great cowboy dinner that takes place in the back country. You can either ride horses to the site or they will take you in a horse-drawn wagon. The cowboys grill steaks, sausages, chicken and serve it with all the sides. You sit around teh campfire or at picnic tables and listen to the cowboys sing while waiting for your cowboy coffee to come to a boil over the campfire. It was probably one of the most fun things we did.
Good luck! Yellowstone National Park is one awesome vacation. Get out of your car and into the woods.