I'm writing this based on my recent and harrowing experience of flying with two infants and a dog. It was a tough day, and by the end of it, I was about as tired as I've ever been, but we survived. Flying with two babies wouldn't be too bad. Flying with a dog wouldn't be too bad. Flying with one baby and one dog wouldn't be too bad (given that two adults were also flying). But I think these tips would come in handy in any of those scenarios.
1. Be kind to older children, for they may entertain your babies.
2. Smile at the flight attendants. Laugh at their jokes. They are the people who bring you spoons and extra water and who hold your babies when you're trying to dig your way out of the pile of stuff on your lap.
3. Sedate the dog. Unless you have the world's most well-behaved pooch, it's just what has to be done.
4. Don't bring any carry-on luggage. You've got to understand that this is coming from a woman who spent an entire week in Paris with only a carry-on. I have never, never, never checked luggage before this trip, but given that we also had two babies, a double stroller, a diaper bag, and a dog to lug around, we would have needed to grow extra arms to deal with any carry-ons in the airport. And trying to scoot down the aisles of the plane with that list of stuff (minus the stroller, which is checked at the gate) was miserable enough. Please, please, whatever you do, don't bring any carry-ons.
5. Bring the stroller and the car seats. Check with your airline, but as far as I know, the stroller and car seats always count as luggage freebies. The stroller can be used at the airport and gets checked at the gate. Then - voila! - it's waiting for you when you get off the plane.
6. Wait until everyone else has gotten off the plane before you try to get up. Just cool your jets. Ha. Ha.