mecabq

All of these airports have transit desks and can suit a return. You wouldn't need a visa (if you weren't checking bags) in any of them, though you would have to go through security -- centralized transit security plus a second security at the gate at DOH and DXB, only at the gate at KWI.

KWI is the fastest transit by far, but with a longer layover (because the plane goes to BAH). In DXB, the plane goes onward from there to DOH and back before returning to IAD, so you have plenty of time. In DOH, with the bus system and transit security, the connection would be tight.

The LH lounge in DXB is the best of these three options, though no showers. There is, however, an airport in-terminal hotel in which you can rent a room for a hour to shower.

(I don't understand why, if you're going all this way, you wouldn't spend at least one night to see the city. To each his own.)