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I am sorry to hear that the Dentist was not able to fulfil the job as agreed because of a 3rd party
I suggest you will want to file a dispute with your Credit Card company based on the promise to credit the money back.
The credit card company should be able to credit your card.
If it comes to a point where you are not refunded, then upon your return to the states, I suggest you will need to file a small claims
lawsuit. And you can do that yourself with the forms that the Clerk of the Court in the county where the Dentist is located. Go there and request the forms.
Hopefully, however, this will be resolved so that you do not have to bring it to court.