Since the credit card was declined, there is nothing to fault AA for I would say ; the complaint is with MDNA

Perhaps look for what reasonable price options exist. Aer Lingus has DUB-LAX r/t in business class for EUR2279 (approx GBP1806) for monday returning friday. Just tack on a UK-DUB flight and will still be quite cheap and a lot cheaper than GBP3700