Gray areas
You should expect Dominican island operations will open as usual on normal business days. However, Freight forwarding terminals operating in Miami will be shuttered for the storm duration. Any item in stateside transit to Miami will be stopped. The land/air carriers will do it to protect the cargo and reduce liability.
If fgt fwd terminals are damaged in any manner preventing them from operating, they usually have contingency plans to notify inland carriers to send cargo to other undamaged freight forwarding terminals, to include those of competitors for ultimate forwarding to the DR. Cargo that is already at the Miami fgt fwdr location will be held for transit to the DR when conditions allow. However, if the terminal and cargo are damaged, most likely the Domincan agent will notify the receivers of what remedies are available and ask for feedback. Note: being real, don't expect concrete answers.
If there is no reasonable response from the forwarder or agent there are some options.
Notify shipper and ask for a refund.
Notify credit card company and ask for refund. if possible
If a cash purchase or cargo from family or friends or other:
With insurance - file a claim.
Without insurance - file a claim with the carrier.
and this is the very gray area. You have to find out who was in possession of the shipment. Was it the trucker, the air carrier, or was it the freight forwarder and beyond ?
In simple terms
The trucker provides a refund, as long as it is not an item of extraordinary value. Refunds on extraordinary value is by formula.
The air carrier will provide a liability refund based upon rate, weight, and taxes.
The freight forwarder is more difficult refund prospect as it has limited liability.
Be aware any claim should include the product, preparation, documentation, and freight costs.
Finally you have to consider an "Act of God". A claim against a carrier can be made if his neglegence to protect cargo in the face of a natural disaster results in damage or loss. That is to say, if the carrier knowingly transports cargo into the storm, not protect it in a safe place, he is liable for the amount what law and regulation allows.
Regards,
PJT