I've traveled by train all over the place and love it! I've done many small trips as well as larger ones--Atlanta to NYC to Boston and back; Chicago to Denver to CA coast to Texas and back; Springfield, MA to Denver to San Francisco to Glacier National Park and back. The last trip was with our son and he loved it, too! He was a bit older (7-8 years old) so he has very fond memories of it to this day. (It's too bad you're not going to take the train from Boston to VA. The area around Mystic, CT is really pretty.)
If I remember correctly, the upper bunks have a little bit of a harness that helps keep your child safe, but I couldn't swear by that 100%. Our son thought it was wonderfully cozy on the top and ASKED to take naps (he hadn't taken naps in years!). Another person also mentioned extra towels or blankets rolled up to provide a barrier which could be a good idea on a lower bed.
Will you have two adults? If so, that will give you a lot of flexibility. If not, people are generally very helpful and friendly on the train--both riders and porters. (My husband traveled with our son back from England to Boston via airplane when our son was just one. People were very accommodating and helpful on the plane and I find them equally so on the train.)
One thing I would recommend is to make sure you venture beyond your little room. Walking up and down the train burns off little kid energy and it's fun to meet others. Half of the experience of the train is meeting all of the interesting people who have the time and inclination to travel this way. Generally the Lounge Car and Dining Car are the best places for conversation beyond your room. As long as you are respectful of people's space, you can also just walk the train from end to end if your 3-year-old really needs to walk. You'll get a lot of smiles along the way.
If your children have special cuddly toys, make sure you bring one for each. Also, books are a godsend on the train as well as those sketching toys where you draw and then wipe it out to start over again (Magnadoodle). Crayons or markers are fine but beware of them rolling under seats, etc. The Magnadoodles are self-contained, without parts to lose. Also, don't forget to just look out the windows and see what is passing.
Our son LOVED sleeping on the train. It's gentle rocking motion and the sound of the tracks were very soothing to him. We didn't bring any electronic devices along with us. We either just sang to him or he sang to us. But if singing is not your family's thing, a device for favorite bedtime tunes might be helpful.
Your meals will be included with your room. But I would recommend bringing some simple snacks if you have the room--goldfish, grapes, raisins, etc. in ziploc bags that don't take room when they're empty. Otherwise, you can buy some snacks at the Lounge Car, but they will cost more than what you could bring along yourself.
Have a wonderful time! I highly recommend taking the train as your kids get older, too. Especially west of Chicago, the tunnels are taller, so you can ride on the trains with the second-level viewing cars. Plus, the tracks are more in the open spaces so you get to see more great scenery!
If you ever do take another trip, the advice I give anyone who is traveling by train is that spring and fall are the best times, with fewer chances of delays. In the winter, you may run into snow delays. Out west in the summer, you may run into heat delays because the 1/2-mile tracks swell, requiring the trains to travel slower for safety.
The other tidbit I recommend on long trips is to work in a day or two layover when you're switching from one train route to another. That is for two reasons. It gives you more of an opportunity to visit new places or to visit friends/family. But it also builds in a little flexibility in case you end up with a delay. That way, you don't miss your connection for the next leg of the trip, thus, stressing you out and potentially ruining a wonderfully planned trip.
Again, enjoy your trip! You'll be surprised how well the bedrooms work for your needs, especially if you think of the entire train as your path for meandering and adventure in visiting. Enjoy!
P.S. I forgot there was a car that had Legos/Duplos, etc. in it. Not sure if all trains have it or not. It was in the same car as the sleeping cars but it was on the lower level. Our son was more enamoured with the trip itself, though. But, remember, he was also older.