OK. Nine days is beyond tight for the non-Barcelona destinations, so we're going to need to know exactly how many nights you'll have available in Spain. Are you planning 5 nights or 6 nights in Barcelona?
For me, Seville should have 4 nights, and 3 is the absolute minimum. The Alhambra takes a major chunk of a day if you want to see the whole thing, so Granada really needs 2 nights so you can see some other parts of the city. Cordoba benefits from 2 or 3 nights, but due to its proximity to Seville and Madrid (and the super-fast AVE trains), a lot of people spend just one full day there (try to avoid just day-tripping), which could be accomplished with one night if you take a really early train to Cordoba or schedule your departure for the afternoon of the next day.
I listed Seville, Granada and Cordoba first because they're a sort of cluster and are more time-consuming to reach than Madrid/Toledo/Segovia. You can easily fly back to either Barcelona or Madrid for another visit, probably a lot more cheaply than you can fly to Seville, Granada or the larger Malaga airport. My first priority after Barcelona would be to do a decent job of seeing the three key Andalusian cities.
By my calculation you now have no more than 3 of your 9(?) non-Barcelona nights left. That's not going to cut it for Madrid, Valencia and Toledo-or-Segovia. I like art (where Madrid reigns supreme), but setting that aside, Toledo is by far my favorite destination among those four. However, quite a lot of what I like about it is the Mudejar architecture, and you will be seeing a lot of Moorish buildings in Andalucía. So--though it pains me to say so--Segovia might be a better choice for you. It has the advantage of having fewer and less time-consuming sights than Toledo, so you might get back to Madrid early enough for a few hours of walking around. Yet Segovia is still very interesting.
You haven't confessed to being in love with Calatrava's architecture, so I'd drop Valencia. As I think I mentioned in my earlier post, traveling Madrid-Valencia-Barcelona takes a lot more time than Madrid-Barcelona, so dropping Valencia saves not only the (inadequate for the city's size) day you'd spend there but also the extra travel time.
This is all just my take on it, and my opinions aren't worth more than anyone else's. And I'm heavily biased toward having enough time in each city to absorb the atmosphere, which means walking around outside looking at things, not just running from one indoor sight to another. Many people are satisfied to go to Cordoba and see little beside the Mezquita.
The trains will generally be faster than driving, and you certainly don't have time to wander around the countryside, so I'd not even consider a car. Parking issues would chew up more time than the few minutes you might save traveling in and out of Granada. Granada is the stickiest destination because there aren't many fast trains going there, meaning you won't have total freedom as to when you arrive and when you depart. You may find a bus more convenient in one or both directions. Check ALSA.com for the bus schedules.
As I alluded to above, there are airports in Malaga, Seville and Granada. If you omitted Valencia you'd end the trip in the south and could explore flight options from those cities. You could arrange to end up in either Granada or Seville. Naturally, Malaga's is the largest airport. I use skyscanner to research schedules and fares for intra-European flights. For preliminary checking on what destinations are accessible from any origin airport, you can either to the airport's Wikipedia page (where you'll find a destination chart by airline) or use the website flightsfrom.
There are sherry-tasting opportunities in Jerez (and also horse shows), which is south of Seville and has decent rail service. You could trade Jerez for Madrid or Toledo/Segovia; I don't know any other way you could include it. I haven't been to Jerez.