Even if your flight schedule won't budge, you can still plan to have a successful flying experience with your kids by doing some advanced planning.
When selecting your flight, it's a good idea to book with the same carrier for the whole trip, or fly nonstop to your destination so there won't be any hassles. Make sure that you follow the Federal Aviation Administration rules related to child restraint systems.
If this will be your child's first flight, you might want to think about a trial run. Take a preview trip to the airport. This can be good for both you and your child. You can map out exactly where you plan on parking and how you'll divide the responsibilities if there are two adults along for the ride. You'll be able to talk through what everything will be like. This can be especially important with security measures -- watching others going through the security procedures makes the process easier. Explain to your kids that they may have to put a favorite toy through the X-ray machine, but that it'll come out safe and sound at the other end.
A few days before you set out on your trip, let the kids help out with the packing process. Allow them to select some items to bring, then be sure to stash some surprises in your bag for an especially difficult part of the trip. Pack extra snacks in case you have a delay, and think about including a reusable water bottle to keep the little ones hydrated.
On the day of the flight, planning is a major key to a good time with kids. Leave enough time to arrive at the airport, park, and go through security. While this sounds like common sense, parents are much less stressed and can deal with their any problems if their patience hasn't already been stretched to the brink. Know where any play areas might be within the airport to allow your kids to work off some of their energy.
Regardless of when you are flying, being prepared can make the experience a better one for both you and your child. Always keep the reason for your trip in mind -- it can make all that hard work worth it.