OK, so now we're getting somewhere! So you'll be in D.C. on a Saturday evening, departing from DCA on Sunday AM? If so, while I won't go so far as to say "there should be no traffic that day", it should be manageable. I STILL advocate Uber, but you CAN drive and, probably, park, though that could actually be a little MORE challenging on a Saturday night than on a weeknight. When is this trip? If it's in the next month, and hopefully the sooner, the better, that makes things a little easier as you'll be here before the full onslaught of tourist season. Once schools start letting out for the summer, D.C. becomes a bit of a zoo, like most other destination cities.

I would still stick with your plan of getting a hotel near DCA given the early departure. Most airport hotels have shuttle vans that can pick you up @ DCA and take you there the next AM. The more I think about this, the more I would skip the rental car and take Uber. You should find plenty of cars available. I would have one take you from the hotel to the Jefferson Memorial, wait for you there if they allow that, and then take you over in the vicinity of the Washington Monument/Lincoln Memorial/Vietnam Veterans' Memorial and then start walking around. You can pick up another Uber (or taxi) and go east to the Capitol building and do a drive by or get out and walk a bit. Then head back to your hotel or grab some food somewhere in D.C.