You would need one of the larger hire companies as some of the smaller (and cheaper) ones do not do a pick up/drop off in different airports. This site is obviously an agent but does do different place dropoffs and looks for the cheaper deal.
http://www.carspain.com/
NOT used them so I can't say if I recommend them or not.
It took me nearly 5 hours to drive from Elche to Malaga in October last year.
New driving regulations? This is Spain ,they make it up as they go along. Don't forget the 110 kph limit on motorways now, though. Hope you've got your high vis jackets, sensible shoes, spare glasses, insurance docs, passports, NIE certificates, the dog's vaccination certificate, the budgie's spare sandpaper, the letter of authority from the local mayor and all the other paraphernalia required before you can even step into the car.