I'm still confused as to what the OP wants. Does he want compensation? If so, I don't think any should be given.

Does he want to expose a "scam" being run by CX? CX isn't attempting to scam OP on the infant fare.

Does he want to the check-in agents to punished? IMO, the handled the matter in a professional manner given the situation. Furthermore, If I had someone not letting me get a word in, while someone else held a iphone at my face I can assure you that my tone would have not as been as controlled as the agents.