Pediatrician's name, regular and emergency phone numbers.
Extra eyeglasses or contacts if you have them.
Medications and prescriptions. Be sure to carry the generic names of medicines with you since the brand names of many medications may vary by region.
An address book with your child's friends' names and addresses so they can send out postcards.
A nightlight to help light up an unfamiliar room.
If your child uses a step up to see the bathroom mirror in your house, you might bring it along.
Items to childproof a room, such as outlet plugs and pipe cleaners. Use pipe cleaners to hold up curtain cords or close cabinets.
If you are traveling with an infant, don't forget to bring a bottlebrush and some dish soap.
Baby wipes are good to bring in the car, as well as little bottles of water.
If it's small enough, bring along your child's favorite toy.
Their blanket, if they are still of the age where a blanket is a close personal friend.
Updated pictures of your children in case they wander off. You'll need recent pictures so others can help you look for them.
Consider packing each complete outfit in separate clear bags. Keeping an entire outfit in a bag will allow them to pick out one complete outfit so they'll have everything they need to get ready in one place. This will help you to organize your packing for them, and also save them time getting ready on the trip. The plastic bags will help with wrinkling. Since all their items will be together, it will help keep them from digging through all your clothes looking for parts of their outfits. They can then use the plastic bags to collect their dirty clothes.
Use freezer bags with a seal for all their little stuff so it doesn't end up mixed in all your clothes.
Put some of your items in their luggage and put some of their items in your luggage. This will give you both something to fall back on in case either of your bags goes missing.
Just as you should with your own, make sure you completely label the inside and outside of their luggage with complete contact and itinerary information.
Extra shoes and an extra swimsuit.