If you want your kids to enjoy reading, just stop over at the Library of Congress located about 12 minutes walking from Union Station. There's something for everyone luckily. Every Friday at 10.30am the Young readers Center has a reading for little kids in a very cozy corner. It gets crowded really quickly so make sure you get there by 10am at least to save yourself a seat in the room. Only 50 people are admitted so it's first come first serve basis.
The reading is one of the few things the kids get to enjoy, there is also a bit of singing and dancing to get them excited. It goes on for about an hour so make sure the kids get their breakfast before they head in for fun because like in all libraries, there's no food allowed.
Once the readings over, you could either leave or stay back for a bit to let your kids play with the toys or take a look at the books over on the stand.