I think Amex travel is clueless on booking children/infrant tickets. I had a similar experience with them, though not as bad and it certainly didnt cost me anything.

I wanted to book travel to have my kid (she's over 2) travel on the outbound with me and return back with my wife on the inbound (My wife was travelling after me and I was returning sooner) The idea was we wanted our daughter to spend more time with the grandparents.

When I explained the situation to the agent, he said that my daughter had to pay the full adult fare. When I said that kids from 2-12 pay 75% of the base fare + all taxes, he wouldnt believe me and gave me a lecture on the fact that he has booking tickets for 14+ years etc. I hung up, called the airline, made my 2 bookings (my wife and myself) online and the (very nice and patient) agent made my daughter's booking on a seperate PNR.

The only real reason I called Amex was to get the extra points and sensing that this moron could screw things up I wisely retreated.

Clearly Amex is starting to go downhill real fast and its agents are completely unaware of children's fare rules, etc. Good luck sorting your issue out.