M.F.
Call your airline about the two carseat thing. However, you might consider taking just one carseat that either the 9 mo old or 3 yr old could use, if possible (the forward-facing booster w/ 5pt harness), and take the baby on your lap. If you need to switch them out during flight, you can.
You'll want to check all your bags, carry baby things in a backpack, and each of the bigger kids can bring a small back pack. Definitely have your stroller with you to push the baby through the airport. You'll just "gate-check" it right before you board the plane. Get a tag from the gate agent, then whell baby right up to the door of the plane, leave the stroller in a small area just outside the door. It's the last thing into the baggage compartment, and the first thing out -- so it is there when you de-plane.
Be sure you take advantage of early boarding. I've noticed flights don't often call for early boarding over the loudspeaker any more, so be sure the gate agent knows you'll need a little extra time to get in the plane and get situated.
Good luck!