Am I responsible, the body shop or my auto insurance if my insurance has maxed on rental car?

I was involved in an auto accident with another driver. The driver hit my car while switching lanes. We are both insured. She gave me her information, I forwarded to my insurance company. I was informed that I could pay my deductible and let my insurance handled everything or go through her insurance company. ... show more I was involved in an auto accident with another driver. The driver hit my car while switching lanes. We are both insured. She gave me her information, I forwarded to my insurance company. I was informed that I could pay my deductible and let my insurance handled everything or go through her insurance company. I called her insurance and was given the run-around, so I decided to let my auto insurance handled everything. They suggested a select service shop that they normally deal with that would offer a lifetime warranty on all repairs. I was given a rental on the 30th of November and my car was towed to the car repair shop on December 1st. I was given a $4000 estimate and promised a completion date which was December 11th. It is now January 6th and my car is still not repaired. My insurance company maxed out on the rental car so now I'm responsible for about $300 that has incurred. The other driver's insurance company is still doing an investigation and refuse to pay anything towards the claim, not even my deductible. I don't feel like I should be responsible for the extra money owed on the rental since I was promised a completion date and my car is still in the shop. What can I do? Should the car repair shop pay for the extra charges since my car is still not repaired way past their promise date or am I responsible?
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