I am feeling a bit confused about the order we should do things when we leave Madrid.
Originally I thought we would take the train to Seville and get a car when we leave. Now, I notice that Cordoba is closer to Madrid---Should we take the train to Cordoba, stay there the one night and then take the train to Seville and get the car at that point?
We would then be heading to Granada and hope to drive through the countryside.

I'd go with spending the night in Cordoba, then heading down to Sevilla the next day. You can pick up a car at the train station when you arrive if you are not planning on spending any time in Sevilla.

Yes, Cordoba between Madrid and Sevilla.

We went to Spain for our 20th wedding anniversary and loved the area you will be visiting. Have you heard about the Paradores? These are historical sites turned into inns (by the government, I believe) in order to preserve them. There is one at the Alhambra that was the highlight of our trip. After dinner we had the nighttime gardens to ourselves. Gorgeous views of city lights, the gardens, and a sweet colony of feral cats!

For visits of towns like Cordoba, Sevilla, Granada, Malaga, Jerez, Cadiz, etc. a car would be an obstacle.
For places in the countryside like the white villages, the Cueva de Pileta, the Cabo de Gata Park, etc. a car would be fine.

Cordoba can easily be done as a day trip from Sevilla: 40 min by train.

Definitely spend the night in Córdoba, much more to the city than the obvious sights. Go some 300 meters north of the Mezquita into Roman Córdoba around Plaza de la Tendillas and Plaza de la Corredera for much more local atmosphere and genuine and affordable tabernas on every corner. Taberna Salinas is one of the more famous, comes recommended in the Michelin guide: http://www.tabernasalinas.com/

In the weekends, the atmosphere on Plaza de las Tendillas is unbeatable long into the night. Several great cafés and terraces.

About Córdoba, "the city that changed the world": http://www.theguardian.com/spanish-t...-changed-world

Thanks so much for relieving my confusion and panic.---Yes, we will stop in Cordoba first, then head to Seville. Does it seem best to take train from Madrid to Cordoba, then train again to Seville and get car when we leave Seville?
By the way, I booked the Las Casas de la Juderia. The Hotel Amadeus only had a suite left. I am feeling good about the choice. I definitely appreciate the help--don't think I could plan as great a trip without it!!

People who know Sevilla usually say that Sevilla is a hell for drivers.
But if you like that, don't hesitate to rent a car at Cordoba.

Yes, train for Cordoba. When to pick up your car (Granada or Sevilla) depends on what you plan to do with it, given that Granada is also easily reached by public transportation.

I stayed at Las Casas de la Juderia - loved it! Hope it works out for you, too.