Booking an infant award fare through AAdvantage for a BA itinerary is not as straightforward as I'd thought. Having travelled on BA with BA miles with our daughter and become used to the 10% rule (miles and taxes), booking through AAdvantage came as a nasty surprise. The infant fare was basically calculated at 10% of the full fare in the cabin - rather different to BA. Although even then there was some inconsistency in what I was quoted by different people on the other end of the phone (in Spain, I think).

After much to'ing and fro'ing, I got the infant fare ticketed direct with BA at the 10% rate as an addition to my own (which had been ticketed through AA).

I remember reading a fair few threads about this on the AAdvantage forum at the time as I attempted to figure out how best to get something sorted out. There were some quite interesting views expressed about the "how awful of you as a parent not to buy your infant a seat of their own"..... but you just have to ignore those.

You will need a lot of patience! No idea what would happen regarding the infant turning two during the trip. It strikes me as rather questionable that you'd be allowed to build in a stopover that goes well into the child's third birthday. Would cause me to raise my eyebrows, that's for sure!