This is tricky and you may need to consult a professional.
Firstly, you have a casualty loss. Losses are only deductible if they are associated with a federal disaster declaration, although I assume the hurricane qualified. The loss is not technically the amount it costs to repair. The loss you can deduct as a result of a disaster is the loss in fair market value caused by the disaster. The typically requires an appraisal. You can use the cost to repair as a fair equivalent to the loss in value, as long as the repair restores the property to as-was condition. For example, if a tree crashed into your master bath, and you take the opportunity to remodel it better than it was, the cost to remodel is not the amount of your loss. One of the methods to determine loss this was is the lower of two estimates. See here for more.
https://www.irs.gov/forms-pubs/about-publication-547
It's important that under this rule, your loss from hurricane damage is based on the damaged to the house, and does not change if a contractor cheats you (or is incompetent) so the repair costs more in the end.
However, could you deduct the loss as a theft? Here, it is important to recognize that incompetence is not theft, and you may need legal assistance. Theft is defined as
"A theft is the taking and removing of money or property with the intent to deprive the owner of it. The taking of property must be illegal under the law of the state where it occurred and it must have been done with criminal intent...The taking of money or property through fraud or misrepresentation is theft if it is illegal under state or local law...You don’t need to show a conviction for theft."
For example, suppose you have damage with a repair estimate of $20,000. Your insurance pays $10,000 down payment. The contractor steals the payment and disappears, and you have to pay another contractor $10,000 out of pocket because the insurance won't cover the theft. Your total loss is $30,000 and you can deduct the total amount since it is due to a disaster.
However, you can't deduct any amounts that are covered by insurance, or that would be covered by insurance except that you choose not to make a claim. Normally, theft is covered by insurance, so you would at least have to make a claim to get the $10,000 deposit covered. Incompetence is also not necessarily theft, and if the contractor botched the job and you had to pay more to fix it, that is almost always a civil matter where you sue, but is not theft where the contractor could be convicted of a crime. A crime requires criminal intent, not merely negligence or incompetence.
So you may want your own professional advice.
