From Traveling With Kids Website -
1. Make sure you eat before going to bed
This might sound a little strange, but one of the things that wakes me (and my kids) up so early when we change time zones, is hunger. If your body thinks it's dinner time or lunch time in the middle of the night, it will wake you up and make it difficult to go back to sleep.
In my experience, eating something before you go to bed (even if you don't feel that hungry) makes it a lot easier to sleep longer.
2. Try to stay awake until it's bedtime
If there's a big time difference, it can be almost impossible for you and your kids to go to bed at the right time in your new time zone, especially the first couple of nights. Try to keep your kids occupied enough that they do stay awake. At some point they will hit the wall (and so will you), and then it might just be best to go to bed.
3. Stick to routines
Try to approximate the bedtime routines from home as much as possible. Bringing comfort items along on your trip like stuffed animals and blankets helps. Giving the kids a bath if they're used to that, reading a bedtime story, singing the lullaby they're used to... it all helps them relax.
Of course, the one break from routine may be that you yourself fall asleep before they do, or while reading them their bedtime story.
4. Keep the bedroom as dark as possible
This also can help both with sleeping longer and falling back to sleep if you or your child wakes up in the middle of the night. With kids especially, it can be hard to convince them that it's night time when their bodies are telling them it's morning. Turning off lights, drawing the blinds and curtains does help.
The biggest challenge I've faced with this is when we go to Sweden in the summer time: the sun barely sets there that time of year, making it look like "morning" pretty much all night long. Blackout curtains are a definite help in that situation!
5. Try to get your kids to go back to sleep if they wake up too early
Adjusting to the new time zone is easier if you try to get your body into the new "rhythm" as soon as possible. If you can convince your child to just lay down for a bit, and maybe get them to sleep or doze for just an extra hour, it can definitely help reset their internal clocks.
6. If sleep is not an option, just roll with it
With kids (and adults too sometimes), the fight to stay in bed until it's "really" morning can often be a losing battle. When my daughter got up at 3.30 am on our first day back home, I got up with her, fed her the breakfast she was craving (I've rarely seen her so hungry, so no wonder she had trouble sleeping!), and let her play and watch some TV while I puttered around doing laundry and unpacking.
Did I wish she'd slept longer? Sure, but it was our first day back, it was a weekend, and there really was no way she would go to sleep right then. Better to roll with it.
7. Be careful with naps
Naps can very easily become way too long when children are jetlagged. This happens to adults too. You're feeling a little sleepy in the afternoon, you lay down "just for a moment" and end up sleeping for hours because your body is out of synch. This is problematic because it makes it harder to fall asleep at the "right" time at night.
After my daughter got up at 3.30 am on our first day back, she did ok until the afternoon when she, not surprisingly, fell asleep. I let her sleep for about an hour, mainly because I knew if she did not have any nap, it would be impossible for her to stay awake until her usual bedtime (or close to it). But after that hour I did wake her up and would not let her go back to sleep. It worked pretty well, though she was extremely tired that night of course.
8. Go outside!
I find that staying active during the day, and especially going outside if it's a nice sunny day, can really help reset your out-of-whack internal clock. For kids, going for a walk, playing in a playground, going to the beach, or just generally doing something that keeps them active does help stave off that tired, droopy feeling that often comes with jet lag.