For some reason, many carriers give families with small children a hassle about preboarding when in a major airport. The smaller facilities, like San Jose, tend to have better customer service.
In regards to your carry-on bags. American allows for 1 carry on and a personal item PER PASSENGER. Your purse is your personal item and the larger diaper bag is your carryone. But you can then claim that your daughters harness/bag (great devices and I use one with my son) and the smaller diaper bag are hers. You should not have had any problems since you met American's policy.
If you have not filed a formal complaint with the carrier, please do so. If you have and have not recieved a reply, please complaint to DOT at
http://airconsumer.ost.dot.gov/problems.htm While we can not get any compensation for you, we can at least ensure that your complaint reaches the correct desk.