What happens if one storm damages both my home and my car in Georgia?

Quick answer: You file two claims, one per policy, even at the same carrier. Some carriers, including Progressive, can waive one deductible when a single event triggers both. If a carrier refuses a covered claim in bad faith, Georgia allows a 60-day written demand and a penalty of up to 50% of the loss or $5,000, whichever is greater, plus attorney fees (O.C.G.A. 33-4-6).