Traveling with Carseat

I haven't traveled with the Advocate, but have with the Britax Marathon. It installs easily on the airplane - look for the lap belt instructions in the manual. It should also be easy in the other car - practice both lap/shoulder belt and LATCH installs before you go.

AS for getting it through the airport - if you're taking a stroller, put the seat in the stroller and sling or let your little one walk. You can also get a $20 metal luggage cart and bungee the seat to that!

The other option is a cheap Cosco Scenera for around $50 - it's much lighter, but is a cheap seat.

We have a Marathon but we never travel with it because it's so big and heavy. Instead we bought an Evenflo Titan, which is much lighter, and take that when we travel. We bought a small luggage cart and just attach the carseat to it with a bungee cord, usually with at least one carry-on bag strapped into the carseat. Until DD was 3 I always wore her in a Mei Tai in the airport unless we were taking a stroller for some reason (but we don't usually travel with one).

I don't have the advocate - but do have the marathon...I have used it at least once a month since my son (now 4) turned 2. I use a carseat attachment called Go Go Babyz (available at One Step Ahead) which connects and has wheels - so I can pull my child (or the carryon) through the airport. If you are patient when installing on the plane, it is not a big deal! As for installing in other cars - I assume that it has latch and is pretty easy to install - wont be much different than when you install in your car.

I have not traveled specifically with your Britax model, but I have traveled numerous times with my Britax and attachable wheels called Go-Go Kidz Travelmate. It is a universal carseat adapter, I think originally made to fit Britax carseats.
The carseat is just fine on the plane, and the wheels are a must have to get through an airport! People stop me all the time to ask where I got them or even to comment that they are a fantastic idea. I bought it on Amazon.

One idea for the schlepping part...

Lengthen the staps as long as they go and then wear it like a backpack with the seat facing away from you. You'll have the hard back against you, but you'll have free hands