It was an error. That's it. Once you apologized sincerely, it should have been nicely explained that you must make arrangements to be on time in the future. What's done is done. Berating you to the point of tears is pointless. Maybe it would have been better if, once the worker started in on you, you had pulled out a little tablet and pencil and asked, "And your name is?????" Then retrieve your child and walk away - straight to the purser's desk. I am sure that you aren't the first or last person to be late for a variety of reasons. I probably would have apologized and if she had been relatively understanding about it, tipped her for her trouble.