It is our understanding that you cannot sue for the cost of your rental car under the Michigan mini-tort provision of MI law.

A mini-tort lawsuit is a remedy in which you can get up to $500 for the damages the at-fault driver caused to your vehicle. You cannot recover for the rental car expense due to the fact that is optional insurance coverage you would obtain through your own insurance policy. You mentioned that you had not purchased this type of coverage as part of your auto insurance policy so you could not make a claim for it with your own insurer.

Michigan law section 500.3135 discusses mini-tort, specifically subsection 3(e). It sounds as if you are using your own collision coverage for the damages to your vehicle so you should be able to use the mini-tort provision to sue the at fault driver for the deductible you are paying out to your insurer to use your physical damage coverage though you cannot recover for the cost of a rental car to use during the time your car is being fixed.