I realize this doesn't exactly fit with your itinerary, but I wanted to mention it because it's such a happy memory for me. My mother and I, and my two kids, took Amtrak from Minneapolis to Seattle and back(to visit my sister) three years ago. We got a family sleeper car with all meals included. We started at night (10/11pm?) from Minneapolis, slept that night on train, spent the day on train, slept second night on train, and arrived in Seattle in the aft. I think.
It wasn't the cheapest but we
all thought it was worth it. Getting there was truly half the fun! The train whizzed through some of the most beautiful countryside - Montana, Glacier National Park, Rocky Mountains. We could sit in the dome car for maximum view, or hang out in our room reading books, playing cards, etc. without having to be seatbelted in.
The meals in the dining car were delicious, and because we had prepaid for them we felt free to Eat-Our-Way-Across-America. We could take as much luggage as we wanted(lots of skiers getting on with full kit) and we had no annoying crowded airport-terminal-type experiences. Our train was not delayed and we rarely even saw another train. I remember one night we passed a lone car driving along a windswept Montana highway while we were at the table in the dining car. I raised my glass of wine to them in a kind of toast, and they waved. I was so glad to be in that train instead of a car like them - I've rarely felt so luxurious in my life!
And I've never, ever, felt so relaxed when traveling with my kids. I'll remember that trip always.