Hi, R..
Even though my profile says D.C., we actually live in Japan. We took our 8 week old on his first flight from Tokyo to Bali. He is now 16 months... and we have traveled a ton with him... when I say "we"... I should say my son and I. My husband comes once and while... we have done the Dulles to Narita route more than I would really care to do... Austraila is even further... ugh.. I am so sorry, but you will get through it.
My child is younger than yours, so unfortunately, I do not have any age specific tips for you from my own experience... but my husband and I do plan to have more. In preparation, I have been keenly observing those expats and travelers who travel gracefully with 4 - 5 kids, and those who barely survive with 1 child.
I do have some general ones:
1. Do NOT overpack for carry ons - see below.
2. For your 2 year old, I would not recommend a stroller for carry on... check it.... A carrier like the Ergo will simplify your life much more... get you through the airports with your 2 year old. The ONLY exception would be if you have a really long lay over in one airport and you think your children will be able to sleep in it.
3. Bring 1 carry on pull on size - you or your husband can pull it. Put your two year old in a baby carrier like the Ergo. You and your husband can each carry a back pack size bag that will fit under the sit. Your 5 year old will have his/her own backpack. You must pack light and think about how you will move through the airport... you do want to carry extra bags... even if the airline allows it... it just bogs you down and complicates things. Before you leave the house actually practice holding all your bags (after the ones you are checking of course)... make sure that you have a free hand so that you buy a bottled water, pay for a hamburger, etc...
4. Do not carry a single toy/entertainment item for your 5 year old. Have him/her pick out a cute backpack... not small roll on... those are too cumbersome as you try to rush them through the airport. Buy one new toy with your help that they cannot play with until they board the flight. Have them pick out their other toys/books, but they must fit his/her backpack.
5. Research your airports and find out where the play area is... if one exists. U.S. airports are horrible with this... since you are flying through Asia... Narita has a FABULOUS play area in Terminal 2... other airports may also have good spots to hang out... just find out ahead of time and take advantage of the airline exec lounges if you and your husband can get in. Singapore is extremely baby friendly and Hong Kong from what I have heard... so do your reserach for lay overs.
6. Be really, really nice to ALL the airport staff and tip well. Take advantage of all porters and curbside check-in. In U.S., there is no curbside check in for international flights... but I will step to the front of the curbside domestic line and kindly ask the attendent to get a porter to help me with my baggage. For a small tip, the porter will take all your bags and take you to best line, etc... no lifting anything and you can check in there without shuffling your 2 kids and all the bags through the maze of rope.
7. Be really, really nice to all the flight attendents and the passengers around you. Do not allow your child to shout or act poorly when first boarding, before take off or early in the flight. You need to the nip the bad behavior before it escalates... and you need to demonstrate to your surrounding passengers/flight attendents that you respect them, too.
8. I said not to pack any entertainment for you and your husband. I assume that you are not flying business class... if you are, you will be set with this next item, but for us... we fly coach most of the time. Bring bottled water, fruit, snacks, sandwiches, etc... I found the only time that I can eat is when my son finally fell asleep and usually I only had 1 hand to eat... so bring sandwiches for you and lots of water...
My last trip with my son, he was 14 months old... he was more interested in the remote control with all the buttons than any toy I brought.... I know 2 is more developed... so I just don't know what to tell you there, but I do know that most people always bring too many toys.
9. Consider talking to your doctor about a seditive/medicine that will make your children sleepy. While I do NOT recommend this on a regular basis... a 33 hour trip to Austraila once a year is different. I wish that you could pop something to sleep... but those days are over since you need to maintain a clear mind... which leads me to my next point:
10. Do not bring any reading material for you... hah! When you are not entertaining your two year old or attending to the needs of your 5 year old, you will be so happy to just breathe deeply and close your eyes for a second or look at the really crazy stuff for sale in back of the seat pockets.
11. Most important: Alter your mindset. I traveled a lot for business and for pleasure before having a baby... I would have a glass of wine.. enjoy my emergency exit seat, pop a couple of melatonin or benadryl, down 2 liters of water... and sleep... Your mindset now is to pack light, pack smart, maintain your blood sugar, hydrate and keep your kids happy. Don't focus on your trip being 33 hours... break it down. There will be moments, where you just need to focus on the moment or you will break down crying... I did that once... it was awful... but with each trip it gets easier. Other times, just focus on 4 hour increments... 2 hours, 8 hours, whatever you need... but don't dwell on the number 33.
12. Prepare your children by explaining what will happen and practice talking in a quiet voice. Explain to them that the trip can be fun, but it will be tough at times and they must listen to you. My 16 month old gets it. He understands that suitcases mean travel and when he is in large crowds, at airports... he listens more attentively and watches my reaction to gauge what he should do and how he should act.
If you need more advice about what to actually put in your carry on, let me know.
Best of luck to you! You will get through this!
E.T.