It's a shitty situation and I'm sorry you are going through it. I also understand being anxious to settle it and get your car fixed. It's important to be patient right now though. Let the insurance companies do what they do. Yes, her story contradicts yours with your company but your story contradicts hers with her company. Both sides are in the same position. Worst case scenario is that you'll be out your deductible to get your car fixed. Yes, you could try going after them in small claims court afterwards and you might win but you won't get the money. Here's why:
Let's say your car has $1,000 in damage and you pay a $500 deductible. Then you go to small claims court and the judge awards you $500 in damages. You just got your deductible back, right? Wrong. You'll have to give your insurance company that money. Why? Because if you don't then you will have been paid twice for the accident. The first payment came from your insurance company and the second came from the settlement. You are always responsible for the deductible amount first so you'll only get your own money back after you've reimbursed the insurance company.
Oh, and don't forget your time spent going to court and the money on court fees. If it were me, I would pay my deductible and get my car fixed while I waited for the insurance outcome. If they find her at fault, then I get my deductible back. If not, that sucks but it was cheaper and easier than court. I would also look for a new place to live.