This is not one of those posts.
I am writing from years of experience dragging our littles across the US and World. Piper's first trans-pacific flight was when she was barely six weeks old. I can't even count how many overnight flights we've made.
The good news is, it gets easier! WAY easier.
After your kids are 4, flying is no big deal. Before that, it's survival.
One thing to remember, all kids have good days and bad days. You are taking your child, no matter their age, and sticking them on an airplane which is an unfamiliar environment. If you are moving abroad, it is likely that you are holding some anxiety of your own, which your kids feel and feed off of. So, try to calm down. If you are calm, there is a much stronger likelihood they will be calm. Or at least calm-ish.
Here are a few of my tips for long-haul travel. If you have any, please share in the comments, and I will add them!
1. Pack snacks and familiar food. As much as adults don't love airplane food, neither do kids. I bring a snack box for each kid (when they are older, you can let them keep it and dole out their own snacks) that is full of as little sugar as possible. Goldfish crackers, pretzels, carrot sticks, frozen Go-gurt, etc. I also pack a peanut butter and jelly sandwich for each kid. Give them comfort where you can. Food is an easy way to do that. Just keep an eye on the time so that you don't run out!
2. I pack two small bags of gummy bears, one each for takeoff and landing. When your ears start to pop, give each kid a gummy bear and let them chew them to pop their ears. Works better than suckers.
3. Throw your rules about screen time right out the window. Yes, pack coloring books and triangle-shaped crayons (Yes, even for older kids. Round ones roll, dude!), play I Spy, do puzzles, etc. You can even print out airplane bingo sheets! But know that if you are on a 13 hour flight, you will run out of stuff to do. I try to withhold the iPad and movie time (God bless in-seat tv!) until after the meal service. That way, if they fall asleep, they have eaten and I have time to clean up the crap we played with first.
4. Don't bring Matchbox cars. I've been there. Made the mistake. Got the freaking t-shirt. We lost two, and of course they were the absolute favorite ones. Those suckers roll, and can be dangerous if they are in the aisle.
5. The kids have played, eaten, and are now settling in to watch a movie. The flight attendants have turned off the lights. When it's about 30 minutes past their non-airplane bedtime, I give the kids a melatonin (1mg) OR a half tablet of children's Dramamine. I asked the pediatrician years ago if there was anything I could do to make long car trips better and he suggested children's Dramamine because it avoids car-sickness and has the joyous side effect of extreme sleepiness. This also works with air-sickness. I give each kid a half-dose, so it's just enough to stave off any tummy problems and make them sleepy. Talk to your pediatrician before you give your kid anything! Also, stay away from Benadryl. Yes, it makes some people tired. But it also makes some kids extremely jittery and hyper, and the effects can be different every time. It can make them tired one time and nuts another. Not a gamble to make on a plane. Plus it is dehydrating, which an airplane already is.
6. The best tip I ever received!! Bring diaper pins with you. Four for each kid. When the kids have put on headphones, take two pins and pin the airplane blanket to the headrest of their seat. AFTER they fall asleep, take two more pins and pin the blanket across the child (as high as you can so it doesn't touch their head) to the seat in front of them. This makes a tent! (If you do this while the kid is awake, I promise they will pull the tent down and rip the blanket. Don't ask me how I know.) As the idiots around you turn on and off their reading lights like a discotheque, your child will remain asleep. If they happen to arouse and look around groggily, all they see is darkness and they go back to sleep. Mine have slept for 8 hours on a flight before. This is AWESOME. I still do it and they are 5 and 8. It also works as a divider on a full day flight if your child is afraid of the adult across the aisle. Sometimes they are seated next to a real loon who won't leave them alone. This helps.
7. For littles, try to keep to their routine as best you can. If you normally eat dinner, read them a book, jammies, and then bed, do it. I always changed my toddlers into pajamas on the plane. It told them it was bedtime.
8. My kids need protein when they first wake up. If yours are the same, get a box of shelf-stable milk from Starbucks at the airport before you board the plane. Give it to the kiddo when they wake up. Again, it keeps to their routine.
9. Water, water, water. Drink water. Buy water at the airport and bring it on the plane so you don't have to be at the mercy of the flight staff. Yes, your kid will have to pee. It's okay. They will get a massive headache and feel like crap if they get dehydrated. Drinking water also helps you get a jump on jet lag.
10. If your kid is making regular kid noises (not talking about yelling and squealing and LOUD kid noises), no one will hear it as much as you do. You are attuned to your own kid and it will always sound louder to you. I remember Piper crying a lot on the flight we had with her when she was 6 weeks old. I was in a constant panic of trying to shush her. When we landed the couple in front of us said, "Wow! I didn't even know there was a baby back there!" All that stress for nothing. Most people use headphones on a plane anyway. And some people just don't like kids and will make faces at you for having the audacity to even fly with children. We do tell our kids to be quiet, and to use library voices, but don't give them a fit about it. You don't want to drive them crazy! If they think they are a constant disappointment during the flight, what good does that do?
11. Pack extra clothes for the whole family. One time, Piper threw up all over hubby right as we were getting on the plane. So now he has an "I love Utah" shirt that is too small for him. I pack an extra t-shirt for me and hubby, and full sets of clothes for the kids. We've used them lots. Whether it's the flight attendant accidentally spilling juice on you, or your kid bumping the tray full of food, or the dreaded potty accident, it's always good to have a spare set of clothes. I always pick stuff that folds up small. Even bringing a set of jammies for the kids is fine. As long as it's something clean.
12. For babies and toddlers, bring their car seat. They are used to it, it is comforting to them, and they will be safe in the event of an in-flight emergency. It also gives you a way to put them down. It keeps wiggly new-walkers in one place and not trying to wriggle free from your lap constantly. They are much more likely to sleep in their seat long term, and you are more likely to get some rest as well. For older kiddos (3+) makes sure they are always seat-belted. When mine were little, I cut the toe off a sock and used the sock-sleeve to cover the buckle to avoid them playing with it, and to avoid it pinching their tummies. Whatever you do, make sure they are always belted in. I don't let my kids sleep on the floor because they aren't belted. It's just not safe. Planes lose pressure. You don't want your kid flying through the air in the event of an emergency.
13. Chill out, dude. Bring your own device that has shows for you to watch, books for you to read, etc. If you have a Kindle Fire, you can download some episodes from Amazon TV for viewing offline. Same thing with iTunes. The first few flights, I packed so much for the kids, I didn't pack anything for me. They sucked. Take care of you as well.
Bottom line, the flight is going to happen. You don't know who you will sit next to, or how many screaming babies will be on the plane, or if your kid will be one of them. Try your best to relax and take what comes. In my experience, the flight is always better than I thought it would be. I prepare for the worst and then am always ready to take what comes!