Santiago rent a car, based in puerto Santiago have good deals tel (0034) 922 861006. Their new web site will be on line in the next few days. I'm not sure if they can do a 7 seater, but it is worth calling them.
All of the hotels and booking agents in the area will arrange a Teide trip for you, book when you arrive.
El Mar coaches (with driver) Tel 922 865991
Hope you have a good hol.