Ignore the lyft/uber folks and rent the car you want - you can always ditch the car at a suitable park and ride if getting into the heart of DC on Metro is critical. You'll be spending a long weekend, not eternity with the car.

If you know where you'll be spending the majority of your time - such as out in Northern VA, Southern MD - set your self up for success and find a) a cheaper suburban hotel with free parking - or free weekend street parking and b) keep an eye out for larger events when you plan your travels for the day so that you don't get trapped in traffic around a specific part of the Beltway and/or DC.

There's MARC and trains between DC Union Station and BWI but, as you indicated, that will add up with three people and eat up time. Keep the car.

Have fun!

David