Insurance claim in this situation

No-fault in MI essentially means that YOUR insurance company will pay for your accident, regardless of who is at fault - it covers auto damage in ADDITION to any medical claim.

For example - Let's say I have State Farm insurance, and I get hit by someone who ran a red light & has AAA insurance. If I'm smart, I call the police immediately & the other driver gets a ticket.

State Farm is responsible to pay for all of the damages to my car, since they're my insurance company. I'm on the hook for the $500 deductible on my policy. HOWEVER - since I was smart enough to call the cops & they ticketed the other guy, State Farm will now make a claim to AAA to get my $500 deductible back since the other party was 100% at fault. The at-fault party is now facing an increase in insurance rates (since they've proven to be a higher risk driver), but my rates are not affected.

The basis for no-fault is to avoid long litigation & finger pointing to get quick coverage after an accident - however, it's more complicated when both parties are at fault or if there's no police report of the accident (since it's harder to prove who is at fault). There are instances where you CAN sue the other person's insurance company, but that's generally in cases of pretty severe personal injury.

SO to answer the OP's question - keeping future insurance premiums in mind, either shop will be fine. If you were not at fault (and have a police report showing a ticket for the other driver & no ticket for you), then your rates will not be impacted by this. Go with whichever shop is your preference. However, I'd recommend that you check with your insurance company to see if there are any dealers you can take your car to - i.e., if you have a GM car, see if you can take it to a GM body shop. At least that way you have a better chance of getting new OEM parts.

Quote from PiratesSayARRR : You are not allowed to subrogate in MI?

Not for rental car costs - only in extreme cases of injury or death. That's part of the no-fault setup.