The part of your post concerning a rental vehicle is unclear. It sounds like you accepted partial payment and therefore may be stuck with the results. If not you can sue the other driver to get what you are entitled to.
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you should send this to your insurance company and let them sort it out first.
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you have a number of issues in this post which are unclear, and which would warrant hiring a NJ attorney to handle for you. Even if it cost you a few dollars, letting an attorney handle this would eliminate all of the stress that you have been going through. What seems stressful and imposing to you, is extremely basic and easy for an experienced car accident attorney to handle, and most likely would have it resolved already, and probably would have saved you money, even after figuring in any attorney fees.
Insurance companies are not your friend, and when you are nor represented, they often take advantage. Hiring an attorney puts that advantage back to you, or at a minimum, levels the playing field.
Each case is fact sensitive, so all answers should be viewed as general advice only, and should never replace a thorough and in depth consultation with an experienced attorney. Further, an answer should not be seen as establishing an attorney-client relationship.
I'm concerned with the "I have NJ plates" statement. Your car is registered in only one state. If it is NJ, you must have NJ insurance coverage.
When you sign for the rental car typically like a doctor's office when insurance doesn't pay, you state that you will be responsible. When the car was called no determination of how much you were covered for or liability would be made so they could not know if the rental would be paid.
This should not be considered legal advice and is intended for educational purposes only. It does not constitute a contract for legal services between any parties. Answers are given to questions for which there may be additional facts not mentioned which might change the legal issues or consequences.
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