I do not practice in your state but generally you have a duty to back out of the parking space with reasonable care and she has a duty to drive through the parking lot with reasonable care. The insurance company can look at the location of the damage on both vehicles and tell generally where you were in your exit from the parking space and how fast she was going when she hit you which will help them determine who was more at fault. There is likely some fault as to both drivers. You should report it to your insurance company (unless the damage is so slight that you would pay most of it by paying your deductible). She may have a claim against you as well. Police don't usually come unless there is someone injured. You should consult an attorney in your area and provide them with all the information you have collected so they can assess your chances of prevailing in a suit. Sometimes the carrier will be more responsive to negotiating a settlement if you have an attorney involved. Obviously you will have to discuss with the attorney the costs of filing suit and whether it is worth it given those costs and what your case may be worth. Good luck.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You have a few options, here. You can turn it over to your insurance company; subject to the $500 deductible; and frequently, they will go after her insurer through a process known as intercompany arbitration. If your insurer succeeds, it will get reimbursed by the other insurer for the full amount (including the deductible) and will, then, reimburse you the deductible.
Another option is to sue the other driver - directly - in small claims court. If you win, her insurer will step up and pay the full amount. Or alternatively, you can have your insurer pay your damage (subject to the deductible) and then sue the other driver in small claims court for the deductible only.
It sounds like you have a pretty good case. It's hard to imagine that this woman will be able to effectively argue that you pressured her into signing the statement. After all, her husband was with her at the time. It's doubtful that with her husband there, she would have felt pressured to sign anything false (unless the guy was a total wimp!).
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