Hotels - look in the crystal city/courthouse/ballston areas and you may get lucky. This is outside the city where 150 may not buy you much. they are easy metro rides into town. Look at renting a car only for the time you need to go outside the city, it is crazy stupid to park downtown right now with meters in effect everyday but Sunday until I think 9 or 10pm. It's not cheap, either
Annapolis and Baltimore are good side trips, Annapolis with a car, Baltimore can be reached via train if you didn't want to bother driving. Philly is a three day trip it's own, min, IMO esp with kids along. It's a destination in it's own right with a ton to see, and 95 is a very boring ride to get there
In your plans for DC, I recommend the Archives and botanical gardens as places often missed. I like Hillwood museum, but not sure if the kids will enjoy it as much as your wife would. Rent a paddle boat outside the Jefferson memorial for an activity, depending on your hotel, they may have bikes to rent/use for the day, as well. There is the manassas battlefields (driving), the air and space near Dulles (drive with pricey parking, but free admission), harpers ferry (drive)
Contact your congressman early to request tickets for the white house .... Really, those are just the beginning of a brain dump. There is just sommuch available in the area