If the AA custodian accompanied the child until they were reunited with you, then I think they met their obligation and a refund of the fee charged would be appropriate compensation. (Vouchers against future travel are useless and often rendered unusable by ridiculous T&C's).
Whilst I agree that their system and procedures are flawed, the degree of inconvenience is relatively minor if your child was safe and was accompanied at all times until she was reunited with you.
The airlines seem to be uniformly terrible at communicating with customers. The internet could quickly and simply answer most questions, but they simply don't put this resource to the best use.
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