I can't/won't defend Hyatt, and haven't a clue what their credit card issue is, but I suggest that you try using Skype (
www.skype.com) for intercontinental calls. We have found their rates to be very, very economical (literally pennies per call, sometimes free), and it has completely changed our approach to similar issues i.e. when we are calling to sort out travel annoyances of the type you are dealing with, or just keeping in touch with family/friends in far flung parts of the world.