I had similiar problems with visa's secure online transaction service when I was buying mileage top ups to upgrade my partner on Singaporeairlines. In the end despite all the phone calls in the world, I had to fax my CC details to singapore so they could do it manually.
I sometimes think those extra security things are just more pain for customers and limits bank exposure. I can't opt out of the visa one with my credit union.
Tell us how your wife found the flight! I fly in first class on Etihad I really love them as an airline, but I hear really mixed reviews from business/economy passengers.