T.S.
I'd bring the 2 year old's carseat along. She needs her own seat anyway, so for convenience as much as safety, you'll be happy to have her belted into a familiar seat. Plus, you'll need the seat when you get where you're going anyway, so may as well.
Nurse the baby on take off and landing (or give a bottle if that's your preference) and bring a straw cut for the 2 year old to help their ears stay clear.
Get to the airport plenty early and plan to have your meal (depending on the time) there that way you don't have to deal with security stress plus parenting in a crowded place at the same time.
Check your bags. Getting two little ones and their stuff through the airport is enough. Let the airline deal with your luggage.
Pack your carry on with a few NEW toys your 2 year old hasn't seen before. (I Spy cards, maze book and calculator have been big hits for my son).
That's all I can think of for now. Good luck.