Expect the train to not be on time, expect some delays on the way there. Keep in touch with whomever is suppose to pick you up in DC and let them know what time you are getting in, because it rarely is the same time the schedule says.
That is the only negative thing I have to say about Amtrack. I have travelled this way my whole life, even taking the train once from San Francisco to Erie. Mostly I have traveled between here and Boston, and you will most likely be on the Lakeshore Limited like I was. You will find that Amtrak passengers are laid back and will strike up conversations with you easily. As a child, I found that there were usually playmates and/or adults willing to play with me to pass the time. Amtrak passengers are used to traveling with toddlers and babies, they aren't as uptight about the noise children make as airline passengers. Bring lots of fresh fruit and other snacks. My mother used to freeze juice in bottles and put them in a small cooler, we drank them as they thawed. We always brought cards, those activity books with lots of games in them, and our own pillows and a blanket. I've never stayed in the sleepers, but I know people that have and they really liked them. If I remember correctly, the cost of the sleepers include some of your food. Plus, it will give you someplace to keep the 3yo if he/she gets a little ornery ;)
Keep your baggage to a minimum, we could never check our bags in Erie because it was one of those stops that didn't allow it, but they do have places for larger suitcases if you think you can handle them between trains. At 8 years old, your child should be able to help you a lot, especially if you prepare him/her for it as an adventure. There is nothing like sitting at the window watching the country go by, places you will never see in a car or a plane. Give yourself and both children backpacks to keep their toys/games/books etc... Your 8yo and you both can handle anoputher two suitcases, and you probably won't need much more if you pack smart. I use to go to Boston for a week sharing a medium sized suitcase with my sister. Consider washing your clothes instead of bringing extra. So, for instance, bring 1-2 pair of jeans and wash them instead of bringing 4 pair.
Have fun! if I think of anything else, I'll edit my post.