Not that it really matters, but what was your routing? I take it that it was international because the infant ticket would have been free on a domestic flight.

There is no compensation due here, but I would expect a significant customer service gesture. I would also expect AA to pick up any additional costs associated with flying UA, e.g., baggage fees, hotel (if overnight required), and so on.

Indeed, if there was an add/collect due, you should have been required to pay it at the counter. But, if you were permitted to board, I am not sure how that failure to collect affects the manifest.

This is one of those unfortunate situations where it pays to be polite but firm. At some point, if a crew member orders you to disembark, you do not have a choice. But, the "ask" so that other passengers are not inconvenienced should be met with, "I'm afraid that will not work for us. Please get your supervisor here."