How do you plan to use your free day in Madrid? If you aren't particularly into art museums, the two days in Madrid may be fairly adequate (certainly better than the one day plus one evening in Barcelona). The itinerary suggests you might want to use the Madrid free day for a side trip to Toledo or Segovia. Those are fabulous destinations worth multiple nights apiece. My preference would be Toledo if I had to choose, but the aqueduct in Segovia is stunning and might be more appealing if you are traveling with children.
The tour skips Cordoba, which is between Madrid and Seville and also worth a stay of multiple nights.
Finally, Seville is worth more time than the tour allows, so if a review of the local sights suggests you're going to miss things important to you, that would be a good place to spend some of your extra time.
In sum, Toledo, Cordoba and Segovia are all important destinations if you don't need to use some or all your extra time in Madrid or Seville. Because of the way the rail lines are set up, if you want to go to Toledo, that will work better as a side-trip from Madrid rather than as a stop on the way from Seville to Madrid.
You can get from Seville to Madrid much, much faster by train (many departures take 2-1/2 to 3 hours) than by car (ViaMichelin estimates about 5-1/2 hours). Those times are to central Madrid; in both cases you'll need extra time to get to the airport by subway, train, bus or taxi.
You won't have a choice of train stations. The fast trains usually only make one stop in each major city; that's one reason they're fast. You'll be traveling from Seville-Santa Justa to Madrid-Puerta de Atocha.
Train schedules can be checked and tickets purchased on the Renfe website: https://www.renfe.com/es/en. Some folks have difficulty using US credit cards on the Renfe website. If it proves a problem for you, try Iryo for tickets between Madrid, Cordoba and Seville; Iryo doesn't go to Toledo or Segovia. https://iryo.eu/en/home. Another alternative--one that will probably cost a bit more--is to buy tickets from TheTrainline.com.
Tickets to all the destinations I've mentioned except Toledo will be somewhat cheaper if purchased well in advance. Be sure you understand the rules for cancellations and changes, however. It would be risky to wait until the day of travel to buy tickets to the cities I've mentioned. Spain is one country where the express trains do sometimes sell out.
I've been comfortable on all the express trains I've taken in Europe. I buy second-class seats.
