So to drive to the top of Mauna Kea, 13 thousand feet, you cannot use your regular rental car. You have to rent from Harpers Rental and rent a 4WD, or there are trips for $200 where a tour drives you up. Has anyone done this. Sounds like the best option would be rent a usual car for the week then on the day of your Mauna Kea trip, drive to Harpers and get a one day rental from them.
http://www.harpershawaii.com/4wd.html