So here is some basic advice based on our experience going to visit grandparents - a trip we've made with one or more children frequently over the last two and a half years. This is admittedly the easiest destination to travel to, since it is a house full of people super excited for our arrival and who love nothing more than preparing for our visit (this certainly reduces our need for an extensive packing list). That said, I think getting through the airport with little kids is a pretty universal experience of hell so hopefully this will be useful to you anyway. But also here is some other good advice from around the internet.
Preparing yourself for traveling with kids
If you are used to traveling by yourself or just with your partner and considered yourself a jetsetter prior to having kids, traveling with the munchkins is going to require some adjustments. The first thing to adjust is your expectations. You will be a lot slower, louder, and messier. That said, if you are anything like me, you may also suddenly acquire a much deeper well of empathy to dip into when stuck behind a family on your next business trip. If you aren't used to traveling all that much, adding kids into the mix certainly doesn't help the pre-travel anxiety. I don't have much advice for you here because we frankly fall into the first category. However, I imagine the best thing you can do is read up on the current rules, think through the day, and talk to more experienced traveler friends.Regardless of your travel experience, I highly recommend making a couple of packing lists. We set them as calendar appointments for packing in the days before the trip, the night before, the morning of, etc. We can then copy/paste them for the way home so as to make sure we don't forget anything while we're away. (The one time we didn't write a packing list, we forgot our daughter's comfort object at the grandparent's house...ouch). We also make sure to pack a change of clothes for everyone in the family (adults included) in the carry-on, as children's accidents often land on adults.
Preparing your kids for traveling with you
The suitcase also allows us to help our daughter prepare for our upcoming travel. She knows that when the suitcase comes out we're going to go on a trip. We let her pick out the clothes we're going to take with us and pack them in the bag (obviously reserving editorial rights for weather and the like.) After bedtime, we move the clothes to the checked baggage and then repack her Skip Hop suitcase with things both of them will need on the plane such as toys, books, blankets, snacks etc.
Why Amazon Prime is your friend
Additionally, Prime comes with access to Amazon Instant Video, which is a fine enough streaming service with one major additional benefit. Amazon (unlike Hulu and Netflix) let you download content to watch offline which means you can let your kid watch things like Sesame Street on your device without having to rely on wifi connections. Note: getting this set up the first time is kind of counter-intuitive (you have to sideload a separate app), so devote 30 minutes to getting it set up sometime the week before the flight.
Day of travel/In flight entertainment
When on the plane we make full use of the pacifier clips to keep toys in easy access of both children. Additionally we re-purposed the old cell phone we normally use as the white noise sleep aid to treat the toddler to some coveted screen time. We come prepared with downloaded Sesame Street episodes (see above) and games. If the device your child uses is an Apple device in these situations, there may be more options for games (here's one recommendation that sounds great) as kids development studios seem to favor iDevices. Our device is an (old) Android phone and our toddler really likes puzzles so she has lots of fun with this game.