If your operate a car as described it'll be for "hire or reward" and subject to a whole host of insurance and related issues.
Even if it was free it would be directly associated with the flight booking, so it'd still come under the hire and reward legislation. And I doubt you could possibly afford to keep/run a decent car just to back up as described.
Just provide a clear caveat on your contract, and suggest that the bride's uncle gives his old Merc/BMW a good clean the day before.