OP bought tickets through Vayama. She thought that the card would be declined, but it wasn't. She (or her now husband) are responsible for the charges. Period.
The fact that it may have taken time for the charge to be approved does not matter. It was 100% her responsibility to call Vayama and cancel the reservation before it ticketed.
Amex has already determined that the charge was legitimate and it's inconceiveable to me that further investigation is going to do anything.
Most likely result is that OP & her husband owe Amex for the original tickets and that Amex freezes the account against future purchases.
Smartest thing OP could do would be to work with Vayama on a credit which can be used on Turkish for specific flights sometime soon.