I flew (alone) many times with my two when they were little. Here are my best tips (in no particular order):
**Have plenty of NONeltronic entertainment. Electornics cannot be used until you reach cruising altitude--this includes time on the tramac. You have to wait to de-ice this can be quite a while.
**Arrive at the airport plenty early:
*Show the 2 year old how security works (watch a couple of people before you get in line). Yes they can flag a 2 year old for extra screening--make it sound fun: "you get to make airplane arms while they wave the magic wand over you IF the beeper goes off."
*Have a light meal (not too greasy--upset stomaches are not a good thing on the plane) after you are through security and shortly before boarding so you do not have hungry (cranky) kids on board. Also stop and buy water/juice to throw in the carry on.
**Find a naerby empty gate and keep the little one moving until boarding time (play Simon Says, Head Shoulders Knees and Toes, etc.).
**Do not preboard. Wait until the end of boarding to get on the plane so your little one does not have to sit for longer than necessarry.
**Pack suckers or gum for ears if your toddlers can handle those. If not, pack the "hardest" to suck though sippy cup and give her something you know she will drink for take off and landing.
**Take twice asmany diapers as you think you'll need.
**Either do not use a car seat for the toddler, OR chose sets of two and two seats right in front of each other. Put someone in your own party in front of the toddler so you do not have to worry about her kicking the seat eahd of her as much (if she is in a car seat she will be able to reach to kick very easily).
FINALLY, relax and enjoy

I have been through some very stressful flight situations with my two (6 hours on a tarmac, stuck in Chicago overnight mid route, TWO planes landing and having to be replaced on the same trip with mechanical problems which included sleeping on the floor in an otherwise unoccupied area of DFW from midnight to 4:00 while they flew in a new aircraft, etc., etc.--NOT that this is normal, we travel waaaay too much

) and in ALL of that the kids have done just fine. They take their cues from their parents so be prepared and roll with the punches and all will go smoothly.