Uber just started offering these last year and claim all the car seats they have (all are one type of seat, the IMMI GO?) expire in 6 years and drivers are trained ("by the Car Seat Lady") to install them correctly.
https://newsroom.uber.com/2014/05/uberfamily-faqs/
Granted, it's all hearsay until I actually see it.
I'd prefer not to park because this leg of the trip I'm on my own with the 3 YO and will have to manage our luggage, him, and the stroller onto the shuttle and into the airport, adding an extra step and additional time. Granted, I'll have to do it on the other end, too, but whatever headaches I can minimize, I'd like to!
I also have fond memories of every time I leave the car at the airport for more than a week, the battery is dead when I get back. At least it won't be dead in the snow like a prior trip!
I do wonder if there are fewer cars available that have the Uber Family option, which was why I was wondering about personal experiences from Dulles. Washington Flyer isn't a great option for us based on where we live (I don't use cabs without car seats, and we don't live near a Metro station).