I agree with all the others and want to add that for the routes involved in your speculative itinerary, the fast trains will get you there much more rapidly than a car. For example:
Barcelona to Madrid: 2:30 to 3:10 by rail; 6:30 or more by car.
Madrid to Seville: 2:30 to 2:40 by rail; 5:20 or more by car.
Another plus for the trains is that all of you can pick up food to eat on the train, saving the time that would be required for a meal stop if you were driving. If the travel situation clears up early enough that you're comfortable buying non-refundable train tickets well in advance, you'll be able to save a lot of money by doing so.
There's a quirk involved in the Toledo trip: Toledo is on a spur railway line connected only to Madrid, so it isn't really "on the way" from Madrid to Seville if you are traveling by train (despite what the map tells you). However, the train is still the fastest way to include Toledo. Many people day-trip there, but it's worth an overnight or two if you can spare the time.
Most of Spain can be really hot in the summer, so if you end up making a mid-year trip, keep in mind the value of having centrally located hotels so you can take an air-conditioned break in the middle of the day if you need to. That's really not the best time of year for Madrid and Andalucia, and Barcelona--though more temperate--can get muggy.
Try to add some additional time to the trip. Two weeks is short for a trip including the places you've mentioned, and I suspect as you continue doing your trip research, you'll start thinking about the Alhambra in Granada as well, plus there's Cordoba--so conveniently located on the way from Madrid to Seville. Even before the pandemic hit, fitting Barcelona into a short trip was a challenge because of the need to pre-book timed tickets to see the interiors of many of its top sights. You must do the same for the Alcazar in Seville and the Alhambra as well.