That's a peak weekend for hotels here, fwiw.

With four, a taxi may not be a bad idea, but if the kids like trains Amtrak is pretty simple -- shuttle from terminal to rail, then either a taxi or the Georgetown Circulator bus from Union Station to the hotel. (The Circulator is more direct than Metro to most points in Foggy Bottom or West End, unless the hotel is further north and thus close to Dupont Circle.)

Anywhere closer to the river will have a great view of the fireworks.