Having flown with 2 toddlers and a baby many many times... and then every age after that as they got older including two 3 year olds and a 1 year old...
here's some advice:
1.) Pay for them to have their own seats. Take their carseats on and put them in their car seats. It will DRAMATICALLY improve their manners (as in, hey, I'm in my carseat, I don't normally get out of it 500 times in an hour...) and is far safer to boot.
2.) FOOD. DRINKS (yes you can bring small amounts if for a child - check your airline first). Lots of snacks. This is SO not the time to be worried about perfect nutrition. Whatever they like, whatever keeps them busy. Okay, for example, one time, we brought 2 feet of cooking twine and a ziploc baggie filled with (organic versons of) Cheerios, Fruit Loops, and some kind of ring shaped pretzel. The toddlers did "make your own necklaces." Then they ate them. I think that was 30 minutes right there.
3.) Mega doses of Vitamin C for several days before and after flying. Yucky yucky petri dishes with wings.
4.) Mess-free, noise-free but still very fun activities. Color Wonder. Magnetic dress-up and story boards. Books. Busy boards (e.g., with locks, latches, etc.). Magnadoodle-type toys (travel-sizes are best). Pack a "suprise bag" filled with random crazy stuff... for a 1 year old, I would pack a little bag filled with a few teethers/small toys, some cool measuring spoons (lol), a soft book, a couple of toy cars/trucks, etc. For a toddler, I would pack different matchbox cars or train cars, a little slinky, a small dolly, etc. Different things for them to reach in and take out and play with.
5.) Divide and conquer. I would seriously consider splitting up. I know it's not very lovey dovey but if you sit in row 4 with the baby, let dp sit in row 10 with the toddler. Switch halfway through if you must. There is something about you getting all uptight and anxious about noise and mess when one of them gets out of sorts and then it just transfers to the kids, and the toddler hears the baby and vice versa... it's sort of a domino effect. So I vote, pack like you're going on separate trips (i.e., separate snacks and activity bags as carry-ons) and then sit separately. AT LEAST don't sit in the same row.
6.) Sling the baby. This is probably stating the obvious, but I always wear the kids through the airport until they're WAY past the point you'd normally be wearing them all the time. I would probably even carry the 3 year-old in an Ergo or other backpack if you have it. It is so much easier to have 2 hands free.
7.) Don't travel during naptime. They won't sleep in the plane. If you can, travel during their "happy time" (morning). Don't wake everyone up 3 hours early to catch a flight. They won't fall back asleep in the car on the way there. It never works. Murphy's Law.
8.) Two words: BULK. HEAD. (This is especially important if you all are going to be sitting together.)
9.) Along those lines, be the first ones there. Line up in the early boarding line. Do this if it kills you. If you have to pee, make dp stand there to save your spot.
10.) Seat the child by the window if you can. That insulates them from whoever is next to you, which is nice for a wide variety of reasons, and gives them something to look at.
10.) Never underestimate the power of the laminated plane instructions. There are MANY things you can do with that little booklet. Lots to look at and talk about.