I don't understand the logic of staying further out to save money on a hotel, only to spend the money on a rental car to take you to a train station. The rental car would only be a hassle to deal with. If you are wanting to make trips to places where there is no train service, save those for a single day, and rent the car for that one day only. Staying close to the rail is very much worth it, because by the end of the day, you are ready to chill out in the room, especially if you have kids. Getting off the train and loading into a car only makes the end of the day seem longer. In addition to all of that, many hotels charge for parking, so that's another cost you might avoid by not renting a car.
Now for other tips.... If you are wanting to tour the White House, write your congressman's office, and request the tour ASAP. They have a limited number of slots open each day, and they fill up quickly (up to 6 months in advance). If you want to go to the top of the Washington Monument go the the National park service website and get your tickets online. They are free, but they are limited too, getting them online will help avoid any disappointment of not getting to do go up. Now, if you can't get a ticket to go up in the monument, go to the Old Post Office. It has a tower you can go to the top in to get great views of the city, and it isn't near as crowded as the monument.
Check in advance on the things you want to see. Some places may be closed for remodeling.
Be prepared for long lines, and security checks to go into all of the buildings.
I would say the longest lines in order when I went last year were...
1)Capitol Building 2)National Archives 3)Natural History Museum 4)Library of Congress 4)Air & Space Museum