Legal Question in Insurance Law in Florida

The contract itself controls. If it provides for the $500 limitation, you wont succeed. Get a copy of your insurance policy and have it reviewed by an attorney.

No. Your carrier is only liable up to policy limits.

With hindsight, you should have reported the situation to your homeowners insurance company and let them handle it. You are basically arguing that since you saved your insurer money by mitigating its (and your) potential liability to the neighbor, you should be reimbursed. Unless there is something very unusual in your homeowners policy, that unfortunately is not the way it works. It's kind of like a mechanic who runs a red light, damages someone's vehicle, repairs the damaged vehicle and then submits a bill for the repairs to his own automobile insurer. It's just not the way things work. Your insurer will likely argue that your actions are a violation of the cooperation close under your policy. They will likely also argue that by acting on your own, your are a "volunteer" and volunteers do not have a claim for reimbursement. Still, it is worth having an attorney who handles insurance coverage issues take a look at your policy.