We used to travel from upstate ny to washington dc frequently. I was homeschooled growing up, so it was considered part of our history lessons. We drove on some trips and used amtrak on some trips, but our trip was much shorter than yours will be.
I always enjoyed it. My youngest sibling was probably around 4 when we went the first time. She handled most of it well, although my mom loved trying to get us to visit tons of art museums and they were not always friendly to families. Many of them wouldn’t allow strollers in at all. They also tended to hover around us with disapproving faces. I am assuming they thought we were going to go crazy and start slashing paintings with knives or something 
We would visit all of the main museums, white house, memorials, ford’s theater. I think we normally took around 5 days to do it all. I remember we would try to get as much done in the morning as possible, and then chill and swim in the hotel pool for the afternoon/evening. That probably helped keep the younger ones happy.
I haven’t made the trip with my own children yet, although I was planning to next year possibly for the same reasons as you.