Personal experience regarding this, and perhaps an idea for those who like living on the edge:
Two years ago, I had a flight on UA which involved both a domestic and international leg.
My child was turning two before the return flight, and my travel agent was not being given clear guidance from UA regarding how to issue the ticket. So, he advised us to purchase a return infant fare (as opposed to a child fare), and worry about any problems if and when they cropped up.
When we checked in on the first segement of our return flight, the domestic segment, we had to show our passports to the agent, being that it was connecting to an international flight. The check-in agent didn't say a word about my child's age, (I have no idea if she noticed the date or not,) and checked us all in, no problem.
At our connection point, we had to show our passports again in order to board the international segment. The agent noticed the date and sternly told us that that we needed a child ticket. With that, she warned us that "next time" we won't be as lucky, and she let us through.
[Ah, that proverbial "next time"; I hear alot about it when flying!
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Good luck!