How best to defend against liability for a car accident?

Question Details:

I recently was involved in an automobile accident. The person in front me stopped to avoid hitting a dog. The owner of the dog was chasing him and I wasn't sure what was going on since she was in front of me; I was looking to make sure there wasn't a child. When I looked up she had come to a complete stop and I rear-ended her. I am battling a divorce now and my ex-husband made some changes so I didn't have insurance on my brand new car (which was a loss and as was hers). The officer listed me as at fault? Can I fight this to get out of paying for her damages?

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