Hi N.,
As my family has been military up until this year, we have traveled a LOT. I have a lot of advice on how to stay sane traveling with small children as I did most of this myself without the benefit of my hubby's presence even though we were both Active Duty. Here goes:
The advice you got about time zones already is solid. Just make sure they don't sleep too much on the flight and they'll be ready to drop the evening you get in. Even if they sleep well on the plane, traveling makes for incomplete sleep. I read a study that suggested that most people don't drop all of the way into deep sleep when traveling so they still need sleep at the destination. I hope that's the case for your children.
Here are a few suggestions:
1. Wear flip-flops or slip ons. It really helps! It's so easy to slip them off at security and back on and it's easy to kick them off once on the plane for more comfort.
2. Pack small pillows for the kids and your own regular pillow and kids favorite blankies. Take a Boppy if you have one, it's great for on a plane and fits very nicely in a plane seat with a small child (like your one year old). It makes a very nice and snuggly little nest for the little one to sleep in and prevents too much rolling so you don't have to worry too much about them rolling onto the floor. Especially if you keep a hand on it when you take a little nap yourself. It's a lot to lug around, but if you bring a stroller, most of it can be hung off of a stroller or stuffed into the basket with your diaper bag very handily. I even manage to hang my older son's backpack (which holds all of his stuff and his blanket) off of the stroller handle too. The boppy fits very nicely over the pulled back canopy. You can use one of those space saver bags (not the vacuum kind, but the rolling kind) on the regular pillows and blankets to make them easier to get onto and off of the plane.
3. Let your older child stretch out on the floor in front of his and his sister's seats for sleeping. Pad the floor with the airplane blankets and lay your own full size pillow on top of those for your 3.5yo to actually lay on and he will be super comfy with the addition of his own blanket. You can use his smaller pillow for your neck and head.
3. Pack about 5 small toys each that your kids have never seen before. They don't have to be expensive, you could even go to the dollar store. Just make sure they have something to hold interest. Like a cup and ball game or those little games where you have to tilt them to roll the balls into holes etc. Give them one toy at a time and space them out throughout the flight by alternating a new toy with coloring or a DVD on a portable player if you have one. Make sure to bring coloring supplies that won't make a huge mess. I recommend the crayola line of no-mess markers and paper. Normally my kids use the regular messy kind because the mess is a part of the fun, but there's no room for the mess on a flight. Also bring regular paper and crayons. Bring a notepad of regular lined paper too, so you and your older child can play tic-tac-toe, or MASH or any number of other simple pencil and paper games. You can even make your own up on the spot with very little effort. You can also use this paper to teach your son how to make paper airplanes, or any oragami you may know. Make sure to bring a few tried and true favorite books and one or two that are new. (I recommend: Where the Wild Things Are, The Giving Tree, Alexander and the Terrible Horrible No Good Very Bad Day, When the Wind Changed, Mouse Tales, Frog and Toad All Year, and of course Dr. Seuss books for your older child and plenty of board books with lots of visual interest for your little one.)
4. I also recommend that your carry on be a backpack as well as your son's. You can split up just about everything between two backpacks (I usually even have room for my purse in mine) and stuff any little extra odds and ends into the diaper bag. Your backpack should be the heavier of the two of course, so I recommend taking the art supplies, DVD player etc. in your own backpack as well as the books and reserving the space in your son's for his blanket, his changes of clothing and the dry snacks. Any drinks purchased in the terminal should be put in your backpack.
5. For snacks take a large plastic ziploc baggie with: another smaller one in it of dry cheerios, Quaker chewey bars, string cheese (the protein is very helpful with diminishing crankiness, and they keep well enough but throw out the leftover ones when you get in), a sleeve of Ritz crackers, something sweet like fruit roll-ups, some cookies if you feel like baking or buying them, and some of the gerber fruit and cereal bars. Throw in anything more specific your kids love that's light and dry enough to go in your son's backpack. Oh and keep the kids hydrated. Air travel is very dyhydrating and that can cause headaches which will make you all miserable.
6. Make sure that the baby had at least two more sets of clothing in the diaper bag (I usually include several shirts, they get dirty faster and they're small enough to stuff several in.) Your son should have one complete set of clothing extra, including sock and underwear, and maybe another extra shirt here too. Here's something most mom's don't think about... pack yourself an extra shirt or two (I usually use T-shirts because they're compact and comfy). Your kids are likely to spill on you a time or two and you would be uncomfortable in a stained shirt. Take one sweatshirt or light jack for everyone, these can double as neck rolls on the plane at sleeping time. Don't forget your kids pajamas. It seems like a lot of hassle to change them into in on an airplane, but they will sleep better with this signal of sleepy time and more comfortably because their pj's are familiar.
7. Finally, pack a small (under the size restriction) bottle of hand sanitizer. You can use in on toilet seats and sink handles and anything you and your children may need to touch that is of a dubious hygenic nature.
I know this sounds like a lot, but if you lay it all out on your bed (or wherever) you'll see that it's really not so bad after all. Most of it is pretty compact stuff and you should be able to manage with two backpacks, a diaper bag and you stroller for carrying all of it around.
Let me know if you need any other advice about this. I feel like my kids and I have spent our whole lives in airports and on planes. :) Good Luck!