Other Insurance Refusing Arbitration, Going To Court?
State: California
I was in a car accident merging into a main feeder lane from a parking aisle. I turned left and an oncoming car hit my rear driver's side panel and the tire area. Normally, I know I would be 100% at fault since the other car has right of way. However, I was in my marked right lane, and the other car was speeding towards me from an unmarked section, and they veered into the middle of the lane, ultimately hitting me. This is how I knew for sure I had completed my turn and not turned in front of them, since my car was fully in the marked lane and theirs was in mine. I was able to record part of our conversation where they apologized, saying they were looking into their back seat and going fast. (this was recorded in a public plaza with no expectation of privacy, thus this recording is not illegal, but I know this still doesn't count as rock solid evidence). I do not have dashcam.
My insurance company found me not at fault, and said theirs refused to pay for damages, so they were pursuing arbitration. I was then notified that the other company refuses arbitration, and that this would be litigated in court. What does this mean for me? Does my insurance company still represent me in court, or do I have to do it on my own from here as in small claims? What are the possible outcomes, and are they affected by how the other insurance keeps dragging it out?