If the performances only take place in Hungary, it's pretty unlikely that US court has jurisdiction.
I don't think this is entirely correct. It's only protected by US law in the US - in all other countries, it's protected by their local laws. That's the reason for international agreements to harmonize copyright between countries, such as the Berne convention.
Only within the US jurisdiction. US law does not superpose or replace the laws of other jurisdictions.
Copyright would probably not be an issue. This looks like a simple contract dispute, a debate re whether one party is abiding a term in a licensing agreement.