You need to speak with a personal injury lawyer in Florida right away. There are many whom you can find here on Avvo. Your lawyer will need to review the insurance policies of everyone involved. Every insurance policy is different and no one can give you advice on the meaning or content of an insurance policy without looking at it. As just one example, my Missouri car insurance does not cover damage in California. For all we know, yours may not cover damages in Hawaii. You can see that there are lots of different types of policies, and your lawyer needs to review the wording to make sure. One thing I can say for certain, though; do not take your own insurance company's word for it that there is no coverage.
That being said, you should amend your post here and let us know if you purchased collision coverage from the rental company (my guess is no?). If you did, then the collision coverage you purchased it will handle it. If you didn't, then the rental company will come after you for the repairs. Because you signed the contract, you will owe the rental company (if you did not get collision coverage from the rental agency). You need to try and get coverage for what you owe the rental company from either your auto policy or your nephew's policy. Hope that helps.
Skilled personal injury to sort out all insurances is your best bet. The stakes are too high to not do so. Good luck.
The author of this answer is an Attorney-at-Law, licensed to practice law only in the state of Arizona. Unless both you and the author have signed a formal retainer agreement, you are not the author's client, and the author's discussion of issues does not constitute legal advice. Opinions expressed herein are solely those of the author, and are neither privileged nor confidential.
Make some calls. Too many issues going on here with several policies involved. The reality is if it is not covered under an existing policy, and you rented the vehicle, and you didn't buy insurance through the rental company to cover, and your nephew was not listed as permitted driver on the rental agreement, you will likely have to flip the bill and get your nephew to hopefully reimburse you. Hopefully, however, there will be a policy for which coverage will exist.
It behooves you to speak to an attorney right away. There are lots of issues that can only be addressed by looking at each insurance policy, your rental agreement, the rental insurance you took out (if any), etc. Good Luck!