I think people have pretty much covered it, but I wanted to highlight a few things.
- In addition to the safety issues, the real problem with getting carseats via the rental car agency is that they're simply unreliable. Too many people have stories of reserving an infant seat and then the only thing available is a booster, or vice versa. Then you're stuck with no good option. Heck, when I rent a car, half the time they don't even have anything close to the vehicle I reserved.
- Taking carseats with you on the trip is quite doable. A few months ago we also went to DC, and we rode the metro from the airport (DCA) to our hotel with 2 kids, luggage, carry-ons, stroller, carseat, and a Pack-and-Play. We didn't even bother rigging up a luggage cart or any of the other excellent ideas that have been noted here; we just piled stuff atop the stroller and carried the baby in the Ergo. We routinely go to/from the airport here in Boston by subway, too. Granted, you will be pregnant at the time, but a cab from DCA to downtown DC is only about $20 if you prefer to make things easier on yourself -- relatively little in the context of the whole trip.
- Others may differ, but I would personally be OK with a mature 4-year-old using a booster, even a NBB, for a relatively short trip while on vacation (as long as he/she is within the height/weight limits of the seat and the belt fits well, obviously). My daughter has been using the Bubble Bum for taxi rides when we're away from home, and it works very well -- the seatbelt is positioned well and she understands the importance of sitting straight. It does help to have another parent in the backseat to help. We also did a "dry run" at home before using it, since she'd never used any sort of booster before.
- Your older child may outgrow CARES (44 lbs.) by the time of the trip, but in that case the regular aircraft lapbelt would be fine. If you are OK with a NBB, that could be his/her carry-on. Then you're down to dealing just with one larger convertible seat on the trip.
- For the younger one, it's probably easiest to just buy a Scenera (or similar lightweight seat) and use it on the trip. However, if you prefer, you could use CARES on the plane and take the metro to your hotel so that you don't need a carseat. Then, during your trip, one parent can pick up the rental car 1-2 hours earlier than you'd planned and truck out to a Babies R Us or Buy Buy Baby in the suburbs, buy a carseat, and install it right into the rental car. When you're done, you can either donate it to a relative in the area (thus using CARES again for the flight home) or use it on the plane and bring it home to keep as a spare. Hertz charges $12 per seat per day for carseats, so buying a seat isn't that bad of deal even if you seldom use it again.