We're kinda going through the same thing right now. Our van got totaled while it was minding it's own business, being parked right outside our house.
After a ****load of talking with both our insurance and the other idiots insurance, they decided to take the van and compensate us for it, in the meantime however, the other guy's insurers would pay for our rental.
We ended up getting a minivan for the next few days until things got finalized. I wanted to drive it back home, but according to the company that rented out the car for us, only my dad and his spouse (my mom) were allowed to drive it. No one else. If they get pulled over and there is someone else driving the rental car, they'll impound it and we're in deep ****.
As for as insurance coverage goes, anything that happens to the car, well the rental company files a claim through your insurance and your insurance has to pay for it. He told us if we paid a little more, we'd have this thing where it's fully covered, and we can bring back the rental car totaled, and neither we, nor our insurance would be involved in anything, the company's insurance takes care of all the repairs.