You're only likely recourse is the claim under your own uninsured motorist coverage (or collision/comprehensive coverage if you have it). Technically the at-fault driver is uninsured and so the coverage should apply. While it is unfortunate, this is exactly what insurance is for. If you have difficulty making the claim, there are attorneys who will assist you in this instance, called a first-party claim.
Case like this are exactly why you should have uninsured motorists coverage. Assuming you have full coverage, your rental will be paid. You can, if you wish, sue the parents for the deductible, if you think the small amount is worth your time to pursue.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-768-3509 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at email@example.com . An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy.
Sign up to receive a 3-part series of useful information and advice about personal injury law.