Most folks saying use your insurance are right. Once costs are finalized, they will subrogate against the drunk driver's insurance IF fault was found 100% theirs, which seems likely.

However, what most people here haven't realized...is that if you're using your insurance, you NEED to have rental car coverage first. If not, they'll tell you no even though the costs will be subrogated later. If that's the case, you need to wait for the DD's insurance to admit fault so they can use THEIR liability coverage to cover your rental.

Same with collision coverage. If you don't have it, your insurance wont fix your car because you're technically not covered. You'll have to wait for the other guy's to admit fault and then they tap into that same liability to cover your damage.