BTDT - don't worry its really not that bad!
We used the stroller to haul the stuff, carseats and kids through the airport. You can gate check the stroller and leave it at the door of the plane, retreiving it the same place when you deplane.
My SIL uses a carseat duffle, it can be used as a backpack or rolling duffle and she is very happy with it.
One thing I want to mention with the 3yo - you "may" want to skip the carseat on the airplane and check it through so you will have it for the ground. I found that by 3 -4 yo the benefits of the CRS decline on the aircraft and it can become a problem. We found that by 3 my dd was to crowded with the carseat. She was uncomfortable, way too close to the seat in front (kicking) and could not use the tray table. Especially with a big seat like a britax you may want to consider checking it with the baggage.
Have Fun
TJ