If possible, the day before you fly make sure that they are physically active. Take them to the amusement park, park, or zoo let them run around.
The morning of the flight, don’t just plop them in a stroller and walk them to the gate. Build in enough time so that they can walk with you. Let them exhaust some of that pent up energy before expecting them to sit still for 14 hours.
If you use mass transit most of the time, make sure that you practice putting them in their car seat and buckling them in over the next few weeks. Maybe put them in the seat when you’re eating meals. On an airplane should not be the first time they feel confined.
Whiskey?
We kids got so geeked and too excited to sleep on Christmas Eve, tradition was that all the kids, no matter how little, got a glass of whiskey before bed.
Worked like a charm, as I recall. 
Lots of entertainment and variety. DVD player of some sort, books, coloring books, favorite toys, new toys, etc. Your oldest may be old enough for the entertainment books sold in airports (fun variety books with connect the dots, coloring and other junk).
I always wore cargo pants and lots of pockets. Keep extra soothers (if using them), wet wipes, kleenix , little snacks, gum, etc. Bring enough snacks so you don’t have to depend on the meal. Bring formula and bottles for the younger one. Order the kids meal at least 24 hours in advance. You want to be able to quick draw some of this stuff.
Benadryl. If you are going to go down this route, definately test a few days before the trip. Benadryl acts as a stimulant for some kids. and some kids are fine with Benadryl only for it to become a stimulant a few months later. You don’t want to learn on the flight the hard way.
YOu should get lots of sleep in advance and have some help when ever you get to the destination.
I’m going to be politically correct here and say that you and your wife should make keeping your kids happy and not bothering other passengers as rule number 1. I think saying “sorry for the inconvenience but we’re doing the best we can.” And if you do that, feel free to have zero guilty feelings if you kid screams the whole way. Do the best you can and don’t worry about other passengers have the hang up that their flying experience should be first class without kids even though they are in the back of the bus.
Choose an Asian airline. The flight crew and Asian passengers ***tend ***to be about 100x more helpful with the bambinas that Hag Air or Northworst. I’ve had plenty of other passengers and even the aircrew help entertain my kids.
Bring a stroller to use in the airport and all the way to the plane. Put your hand carry and other crap in the bottom. Gate check it and wheel that sucker all the way to the plane door.
The layover can be kinda hellish. Go find the kids play area and camp out. SF has a pretty fun kids area.
That’s all I can think of now.
Ah, some good ideas here. I think the idea of us getting lots of rest ahead of time is one on the things I didn’t think of.
We’re going to cut down on how much carry on luggage we have, but will take plenty of distractions for the kids. I’m thinking of taking a lot of sponge toys since they compress well.
The kids like bananas, we’ll take plenty of them, as well as the extra formula, etc.
I’ll try Benedyl out ahead of time. On myself. 
I may even try the shot of whiskey ahead of time.
I’m also thinking of taking something which makes a fair amount of noise and letting them play with it in the restroom to let off steam.
Wearing out my daughter before the flight seems like a good idea.
If whatever you try doesn’t work, please do not be offended or refuse if a fellow passenger offers to buy the kid a shot of liquor.
Or Dad! 
About 10 hours into a really horrible flight on United, my 2 eldest kids were settled down and/or sleeping and my autistic daughter was *finally *sleeping, the air crew came by and gave me 2 mini’s of Jack Daniels on the house. She thought I had earned it.
One other tip for the OP, you can got to the air crew station and just add hot water to the bottle. I mean ask first, but they were always cool with me doing self serve. Also, during the layover, Starbucks can fill the baby bottle with hot water as well.
Would it be really tacky to buy some cookies for the people in the rows ahead and behind up? Tell them upfront that we will do our best to keep the kids quiet and leave out the “but we can’t promise anything”?
Thanks for the tip on Starbucks, China Guy. Good idea.
Next, any tips on how to let toddlers work off steam for that many hours? Letting my 13 month old boy walk quietly up and down the isle should be OK, but having a three-year-old run isn’t cool.
As a passenger, the biggest thing I care about is that the parents are engaged and doing their best. Not that Satan’s Spawn is acting like, well, Satan’s Spawn. I would hazard a guess that most parents traveling on the flight feel generally the same. Do your best and don’t let 'em run wild while you take an ambien and sleep for 8 hours.
As a parent with little kids on the flight, I try to minimize the discomfort of those around me, and feel zero guilt about a big FUCK YOU to anyone that has a problem with kids acting like kids. After a few hellish flights, we’re talking twins doing tag team screaming for 14 hours, I apologized to a few fellow passengers and they were most gracious (“Christ, you shoulda seen my kids” or “I have kids and totally understand” type thing). I have had a couple of fucktards who thought they were entitled to first class treatment for an $800 international ticket. But generally, virtually everyone is cool with it. My WAG is that US domestic travelers will be the ones with an attitude about it and the international flights are fine.
On my last flight back from the States, from Dallas, the family across the isle from me had brought absolutely nothing :eek: for their 18 month old, and both of the parents wanted to nap at the same time. It could have been their third leg, but still. . .
I was improvising toys out of the plastic ware just to keep the guy busy. . .