If you haven’t already check Autoslash for rental car deals. Sorry you’re dealing with this.
In Michigan, the only thing you can recoup is any medical claims and it would need to be a suit directly with the other driver, and not their insurance. The other driver’s insurance company is not obligated to you.
Get that rental on your insurance coverage for next time. It’s only a few $ a month. You can also ensure the dealership you lease/buy from and that you have repairs done at has a loaner program. You can also go find a shop that provides loaners that isn’t the dealership, but hindsight is 20/20