International plan

Prepaid roaming with the $35 add on works in limited countries.   

Aruba is not covered... 

https://www.att.com/prepaid/static-pages/intl-travel-add-on/

You will have no service, other than possibly Wi-Fi calling.  Wi-Fi calling works as if you were still in the United States and is billed as you as if you were still in the United States. That means calls to other us numbers would be free. Calls to numbers in Aruba would be charged as long distance

add the international plan to my wife’s phone

The only international plan that would function would be a long distance plan which would make wifi calls to numbers in Aruba less expensive. Wi-Fi calling still works if you are calling back to the United States.   

and to resolve some charges from my wife’s iPad

If your wife's iPad is on prepaid it is not capable of incurring charges. There is no prepaid plan that allows roaming outside of the USA. If your wife's iPad is on a postpaid plan, you should turn it off and use it as a Wi-Fi only device.  It's likely not covered by a roaming plan, or a roaming plan that's very expensive, with overage charges.

What do you mean by isn’t working? The international plan only controls how much you pay to roam. If you are not getting service at all, it is something else, not the international plan.

Not enough information.

1.  Are you prepaid or postpaid?

2.   Did you add the $10 travel day pass to each of your lines before leaving the United States?

3.  No?  What international plan do (you think) you have?  

Yes I’m prepaid. I have no cell signal, no ability to make any calls. I spoke with an AT&T rep yesterday by dialing 611, to add the international plan to my wife’s phone and to resolve some charges from my wife’s iPad and shortly after that I lost the ability to call out. Calls immediately fail. There’s no ringing and there are zero bars for the cell signal.