General Principles
Two general principles come into play when trying to optimize flight boarding with a toddler. First, never check bags or allow your bags to be taken from you. Even without a toddler, checking a bag extends the amount of time spent on air travel by a considerable amount. Relative to carrying-on, checking bags requires time spent in an extra line at the beginning of the flight and time spent waiting at the baggage carousel at the end of the flight. Add to this the fact that airlines frequently lose bags or allow their employees to pilfer the bag's contents. Checking bags is never a good idea.
My second general principle - minimize the effective flight time for the toddler. Unless the parents have significant pull with air traffic control, they cannot do much to control the actual flight time, defined as the time from when the airplane door closes at the departure airport to the time when the door opens at the arrival airport. Parents can, however, influence the effective flight time for their toddlers, which I define as the time from when the toddler enters the plane until the time he or she leaves the plane. Regardless of whether the plane is actually proceeding towards its destination, if the toddler has to sit in a seat the toddler's parents need to expend their limited effort, energy, creativity, books, and food to keep their child content. So decreasing the actual time spent on the plane can dramatically increase the overall comfort for both the parents and the toddler.
Packing for Success
I may expand my upon my thought process for optimal packing for traveling with a toddler in a future post, but for now I will just describe how we pack for flights. We usually travel as a group of 3, two parents and our child. This means that we can carry-on two larger bags, which we place in the overhead bin, and two smaller bags, which we place under the seat in front of us. For the two large bags we use one large wheeled suitcase and a large hiking backpack, both obviously need to fit in the overhead bin. For one of the two smaller bags, we take our diaper bag, which is also a backpack. This leaves us to take either our computer bag, mom's purse, or another small bag as our second small bag depending on the circumstances. This works well for traveling through the airport since we carry two of our bags on our backs, drag one behind us, and can either carry the fourth bag or strap it hang it on the wheeled suitcase leaving 2-3 hands free to deal with the toddler.
Our Technique
So here is how we do it. In order to ensure that we can find space in the overhead bin for our larger bags, one parent, lets say Dad, boards the flight as soon as possible to find space for the large backpack and the wheeled suitcase. Hopefully we have frequent flyer status on the airline or have arranged our seats to allow early boarding. Regardless, the best way to ensure overhead space is to board early. Boarding early has the downside of increasing the effective length of the flight for the toddler. So to avoid this, the other parent, say Mom, stays in the terminal with the toddler until the last possible moment before the doors close. On extremely full flights like the ones we had over Thanksgiving and Christmas, this can delay the time when the toddler has to enter the plan by 20-30 minutes, which is significant even on long flights.
As you execute this technique keep a couple points in mind. First, technically this technique violates the airlines' policy of only allowing each passenger to carry on one large bag and one small bag because Dad carries two large bags onto the plane. So to avoid having an issue with the gate agent Mom should stand in a location where Dad can easily point her and the toddler out to explain the situation. We have actually tried having Dad carry three bags onto the plane, but were stopped by a gate agent and told to leave one bag (luckily a small one) with Mom. So we think the best approach is to avoid contact with the gate agent by having Dad only take two bags. This leads to the second point. Carrying on one wheeled suitcase and one backpack helps ensure that the process works. I cannot imagine that an agent would let a person carry on two wheeled suitcases, but agents are much less likely to notice both the wheeled suitcase and the backpack are "large" bags - especially in the rush at the beginning of boarding.
Again this has worked very well for us on our last four flights. Cutting down effective flight times by 20-30 minutes makes for a much more pleasant flying experience. Hopefully this information will help!