Rick's top sightseeing suggestions are right on this website: https://www.ricksteves.com/europe/spain. Click on one of your target cities under "Places", and then click on "At a Glance".
I agree that Seville, being the largest of the Andalucian cities, needs more time than the others.
On such a short trip it's a real shame to have to check into Madrid hotels twice. It's not a good use of your precious time. And if, like many of us, one or more of you is sleep-deprived/jetlagged on arrival day, that day's going to be a total loss if you hope to use it for sightseeing in Madrid. This is the logic behind the suggestion that you move on to one of your other stops on arrival day. That is really only practical/safe if you take the train rather than driving on this itinerary. But it makes great use of otherwise nearly-useless (for many travelers) time on arrival day and makes your last full day a great one for sightseeing in Madrid, without having to worry about getting back there from one of your other stops.
Americans tend to assume a car will be faster, but between major European cities that's usually not the case. Your route involves under 9 hours sitting on a train, versus an estimated 13-1/4 hours by car. That driving-time estimate is from ViaMichelin and does not allow for stopping, getting lost, traffic tie-ups or looking for parking. Realistically, you'll be spending close to 2 of your 9 days sitting in a car if you choose to drive. On a train you can at least enjoy a lunch or dinner you've packed.