Please don't waste your hard-earned money (almost $12,00 for a family of 4 !!!) on ABD to Philly & DC (I live here). They are very easy cities to tourist in. It's a quick Amtrak train ride between the downtown stations in the two cities; don't drive, you won't need a car to sightsee in either city.
All you need is a plan: a list of attractions you want to visit, a centrally located hotel to walk to attractions, maybe a HOHO (hop on/hop off) bus or METRO (subway) ticket for things bit out of the way like Arlington cemetery. Remember that all the Smithsonian Museums in DC (Air & Space, American History, Natural History, National Zoo, etc) as well as other attractions like the Capitol (get tickets ahead of time) are all free; in Philly, National Park affiliated places like the Liberty Bell and Independence Hall are free. Both cities are super family friendly and have great off the beaten path stuff to do and places to eat. Take your time and see a show or a sporting event; wander some of the great neighborhoods and get a feel for two great cities. Enjoy seeing and lingering over what your family in interested in.
Gettysburg is very worthy of a day trip from DC. Rent a car for the day through your hotel; it's about an hour and 45 minute drive and you'll see some lovely countryside on your way there. Then hire a National Park ranger to join you in your car for one of the best tours ever. Those three days of the Civil War battle in July 1863 will come alive as you walk that hallowed ground.
Every kid should visit these great places; plan it as a family...