Hi A. --
I have twins. And we had to fly with them several times. I'm sorry you have to do it alone, b/c it will be difficult.
Since your baby will be on your lap, I'm presuming you paid for a seat for your boy. Since he's entitled to check luggage, you should check his carseat. For your own convenience, check the baby's carseat too. It will just count as one of your pieces of checked luggage. You can pack your clothes and the two kids' clothes between two suitcases and check them. If your son is very active, and you think you can handle it, carry on his carseat. When my twins were 20 months old, we carried one carseat on the plane and sat one child in it while the other was a "lap child". The one in the carseat sat still and was easier to handle. Just my two cents.
You can then put both kids in the stroller and bring the stroller right up to the plane. At the plane, they'll take the stroller from you and store it, and then it will be right off the plane when you get to your destination.
If you have or can borrow a portable DVD player for the plane, that will help too. We watched endless Wiggles videos on it. And the plane is so loud, no one was bothered by it.
Also, snacks. Bring lots of different kinds of snacks, and make a game out of it. Like, "five more minutes until the next new snack."
Your baby should be a breeze. Mine slept on planes easily. Make absolutely sure she is drinking something on takeoff and landing. It's necessary for her ears.
I wish you well on your journey.
I am the president of the Mother's Club of Hernando County. If you are interested in making new friends for yourself and your kids, we'd love to meet you. Send me an email (____@____.com) for more information.
Good luck,
-- C. king