The Yampa is awesome. Two years ago was my first time and now we try to hit it every year. Really the only rapid of concern is Warm Springs and it is fairly straight forward. There is a trail across the rocks on river right to boat flip eddy so if you are concerned about the kids they can be walked around. The day section down the Green is fun bouncy wave trains.
Lots of cool stuff to see; caves, pictographs, side canyons; the Whitis river map has some info on side attractions etc. The hike up Bull canyon from the Harding camps is a must do as is the hike to the pictographs from Jones Hole (on the Green) taking in the "butt block" waterfall along the way.
This is helpful when choosing campsites;
you make requests and get what they give you. I think we got 3 of our requested 4 last year and thank goodness got a Harding that we had not requested; we had completely missed the hike to the rim on the previous trip!
When is your launch? We have June 4th.