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.
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