At the very best, the OP got to bag drop AND gate at the very minimum requirements. There is clearly discussion as to whether AA jumped the gun by 2-3 minutes and I'm not sure who is correct. OP had a stroller and little ones usually slow folks down and distract them. From what I read, they weren't ready to board, making the unfortunate false assumption that the phone absorbed guy in front of them was in line. All the ATL based costs OP incurred were unilaterally decided and AA is not obligated to pay these. OP asked for advice. I would advice to get to bag drop and gate more than a minute or two before the deadline (or possibly in this case a a few minutes after the website recommended times), especially when traveling with children.