check it before I wreck it... : )

Suggest you pick up rental car as you leave Sevilla. Visit Cordoba by train as a day trip.

Madrid's major sites are compact, it is walkable and safe. Both routes for Hop on/off bus give a brief overview. Madrid to me does not feel like a large city until you take the Metro to the airport with everyone going to work. Toledo may be done as a side trip from Madrid. Seville tourist area is compact and busy with tourist. It is a big city. Tickets for sites may be bought without standing in line but for only a brief moment. Walking distance increases slightly in comparison to Madrid. We saw the three major sites in Seville in one day and two nights. I would suggest decreasing your stay in Seville unless you plan to day trip from there. Consider Ronda access and/or distance with a car is better from the coast. We drove to Ronda from Granada (it is an all day drive) and continued toward Malaga after a two night stay. We had more days for our trip. Depending on the route it can be a hold onto your seat ride.

AutoEurope for rental car.

I always rent from Avis, but that's just a personal choice.

Very near Sevilla is Italica. It was built as a retirement city for Roman soldiers who didn't want to return to Rome. Very nice ruins. Depending on how far you want to drive, both Cadiz and Jerez de la Frontera are about an hour south. If this is your first time to Sevilla, there are enough things to see in the city that you won't necessarily need to go anywhere else (assuming you see things at a nice leisurely pace). Essentially, I wouldn't rush Sevilla just to see something outside the city.

If you're near Ronda, then you may as well spend some time driving at least a couple of the white towns. Arcos de la Frontera and Zahara de la Sierra are my favorites, but there are others worth a drive by. If you like driving touristy Spain, then continue down to the coast and drive it between Marbella and Malaga. Not much of the real Spain left there as all the town cater to tourists and Ex-pats living in Spain. East of Malaga is Nerja that many find worth a visit although i haven't been there. Along the coast at about the spot you'd turn north to go to Granada is Salobrena. It has a nice beach.

Nice job. Great trip.
No need for car though until you leave Seville.

Day
1..land in Madrid 7am (2 nights)
2..Madrid
3..train to Toledo (2 nights)
4..Toledo
5..train to Seville (4 nights)
6..Seville
7..day by train to Cordoba
8..day by train to Jerez/Cadiz
9..pick up rental car. drive via Arcos to Ronda (2 nights)
10..Grazalema + Zahara
11..drive to Granada (2 nights)
12..return rental car. Alhambra
13..fly from Granada to Milan

I agree with the great minds here - don't get the car until you're ready to leave Sevilla. I think your plan is not just realistic, but excellent.

The only adjustment I'd suggest is to consider going to Toledo first. Arriving after a longhaul overnight flight, a small town, low key place might be better than the intensity of Madrid.

For European car rentals, I start with Auto Europe (consolidator). Then I check the companies they show and compare prices - be sure to read the terms & conditions. Sometimes things included in the company price are not included in the Auto Europe quote. With Auto Europe you have to pay when you book, but in my experience they are prompt with refunds if you cancel.

Read this article about using trains. You can save a lot by buying your tickets (no refund, no change) when they first go on sale, usually 62 days in advance. For a day trip from Sevilla to Cordoba, you could save €10-15 on each ticket, that's €40-60 for a couple.