Auto Insurance Claims: Need some suggestions.., insurance agent, left turn

Question
What happened in the accident was that I was on a two-way street in a mall parking lot trying to turn LEFT.  A girl was at a stop sign trying to make a LEFT turn.  I had my blinker on, attemped to take a LEFT, she pulled forward and hit my vehicle.  I report both insurance companies right away.  She did not call until a little over a week later and explained to the agents that I cut the corner too close and hit her car.  Both agents suggested that I should just go ahead and use my policy to fix my vehicle because according to her story it's a conflict and they cannot determine who's at fault therefore her insurance company cannot accept liability.  I knew for a fact that I did not cut the corner too close, she's making a false statement causing me time and money (having to come up with $500 for deductible) dealing with the whole situation.  My insurance agent suggest to go ahead and fix the car then we can deal with trying to collect money from them.  Including some pictures evidence that may help us.  He mention something about arbitration.  I would like to know what are the good chances that I'll win once we go into the arbitration process?  I feel that if she can come up with a good story like this... this can happen to a lot of people out there too.  I'm just trying to get things right, that's all.  Any suggestions would help... so far nobody can answer my questions.  Any past experiences like this that you know of that you could share?

Answer
If your insurance company has handled the damages, you will be best served by allowing them to handle the rest of the process.  They should get pictures of the damage on both vehicles and may be able to determine some of the liability with that info.
Without seeing all of this info, including the scene, I cannot begin to guess on the outcome.
Good luck!