I've been an expat for over 10 years, and our two children, ages 2 and 4, have been on countless fights. I say countless because I've honestly lost track of how many flights! One of these days when I'm not busy starting a new business, I plan to sit down and figure it all out.
My son's first flight was at age 3 months, and I was flying alone with him from Kuwait to Toronto with a connection in Heathrow. It was tough, it was stressful and there were tears, not just from the baby! Luckily, I met a lot of kind strangers that helped us through.
I'll never forget when we landed in Heathrow for our connecting flight and the airport staff told me that my carry on luggage was too big. This was mind boggling because I had just taken it off of a plane! She told me that I would have to take out my 'needed items' and check the bag. NEEDED ITEMS! I was wearing an infant on my chest and pulling a suitcase, how was I to carry these 'needed items'. I quite calmly told the lady that I would not be checking my bag because the items I needed included diapers, wipes, bottles, toys, clothes, blankets, books, snacks, socks, headphones and a hoodie. Her response was...'OH! Okay have a nice flight."
On another occasion, my sleeping infant had just fallen asleep in the stroller, and they wanted me to take him out to go through security. I begged them not to make me disturb him, so they kindly obliged and used their wand to scan him and the stroller instead of putting it through the machine.
The moral of these stories is don't be afraid to try to reason with the airline and airport staff. Sometimes they are just so used to 'doing their job' that they forget to be a little compassionate. I have found with gentle reminders (and sometimes tears) they can usually find ways to be helpful.