Welcome to FT!
I don't believe there are any hotels with shuttles to both airports.
If I were a hotel close to DCA, it would be a very expensive undertaking to run a shuttle to IAD.
You will need to take public transport or a taxi to DC to pick up your car.
Why aren't you renting from IAD?
Last edited by UAPremExecflyer; Jul 3, 2012 at 8:34 am
Reason: added rent from IAD?