Ideas for car travel.
Having rented cars several times in Spain, I make the following observations. Driving in Madrid is brutal as compared to a typical city in the US. There is a tremendous amount of road construction and detours are long and tricky because cities are rarely grids. Parking can also be expensive, difficult, and lead to minor damage such as door dings, dents that you will later pay for.
That said, consider this: Enjoy Madrid on foot, metro, and taxi. Take the train to Toledo. Rent a car from there and continue on. I drove from Madrid to Granada via Cuenca, Almagro, and other towns, returning a slightly different route including Ballesteros de Calatrava. The small towns are worth the stops but I advise having advance reservations that include parking. In Almagro, the owner of the hotel allowed me to leave the car in front of the hotel even though this was a no parking zone. He said, "Leave it. It will be fine." It was fine, but not something I am comfortable with.
Seville is also under reconstruction and you might consider leaving the car at the airport, visiting the city and then picking it up again. I did this in Granada, where I parked in a lot that was reasonable and secure.
Renting at the airports or train stations and heading off in the car may lead to extra fees and extra metro or taxi rides but it is usually very reliable, easy, and connected to major highways that will conduct you toward your next destination with less traffic initially. And who wants to start a journey with an hour of stop and go nonsense?
Enjoy the ride, that's what it's all about.
El Almirante