Went for the first time a couple of years ago and went back the following year as I just didn't get enough the first time. It is a fabulous place as is Grand Teton. Advice above is pretty much on target. First be extra careful with your food and don't leave any around your camp. There are gear boxes in most camp areas. The Cody museum is nice but to me no where near the sights of the drive from Cody to the park and the park. Be sure and take your binoculars and a spotting scope if you hav one. My three favorite parts of the park are Lemar Valley, Hayden Valley and the geyser basin at Old Faithful.. Grand Prismatic is also beautiful but to really see it you have to hike and climb a steep ridge behind it. Don't know how old the kids are but it is a hard climb.
While in Lamar your best chance to see wolves is early or late and there are folks that will be set up along a ridge line to watch for them . There was also a den in Hyden and a lot of folks set up at the pull offs there with spotting scopes ask around to find out where they are being spotted. We did see moose on the drive from Cody but the most we saw were in Teton along the road to Gros Ventue and on Willow Flats. If you get to the ge Teton don't miss the Bend area or Cattlemans Bridge as it is beautiful. We also enjoyed the wildlife art museum in Jackson. Oh and one of my best meals ever was sitting in the lodge at Grand Teton looking at the elk and moose on Willow flats while eating eggs Benedict for breakfast. Enjoy