who is supposed to pay this claim?

I was rear ended at a stop light by a sarasota county (florida) van that was rear ended by a rented vehicle (alamo). both my vehicle and the county van were at a complete stop for over a minute. after several days of getting the run around from alamo, they gave me the adjuster of the insurance company (travelers) that the renter has because the renter did not purchase alamo's insurance. Travelers is now giving me the run around and telling me that they might not cover the claim because the renter has been in several accidents in the last couple months. What happens if travelers denies the claim? Who do I have to sue to get my vehicle repaired? It is going on 3 weeks now and alamo, travelers, and my own insurance company (geico) keep pointing the finger at each other. frustrating!