We took the train to Portland last weekend, the first Amtrak train trip for both Caitlyn and myself (Ian's done most of the West Coast by train). I've taken trains in Europe, but this was the first non-light-rail train trip in the States for me. And I might just be a train convert. Significantly less stress than flying since there were no airport security tactics and more comfortable than driving. Caitlyn got to play with other kids on the trip down and entertain someone else's grandmother on the trip home - all while not being strapped into her car seat. I actually got to read a book. And it was fun to look out the window and not be watching traffic. The tracks periodically paralleled the highway, but we also got to zip through forests, a couple of tunnels, along the sound, and through the back edges of various towns.
I do have the sense that we were lucky and had fewer delays than is "typical"... but we also deliberately scheduled train times so that if we were delayed for a bit, it wouldn't hugely impact plans at our destination. Another good reason to travel with a cell phone; you don't have to worry about people waiting at some station for you, wondering how to speed up a delayed train.
I'm likely crazy, since I was never able to sleep well on European trains, (Somehow, the sound a train makes as it chugs through the night is similar - to my brain - to the sound an earthquake makes just before it starts shaking you. Add to that the rocking that a train does and a bunk that always managed to be about 2 inches too short and I simply could never fall asleep.) but I'm actually thinking that perhaps taking the train for longer family trips might be ok. Can you Amtrak to Yellowstone?