Southern Spain Itinerary March 17 thru April 3

I've been to Madrid, Toledo, Granada, Cordoba, and Seville. Haven't been to the other places you mention. I like your allocation of nights, except that I would add an extra night in Madrid so that you have 4 nights instead of 3, especially if you like art museums. Madrid has some outstanding art museums. We visited the Prado and Reina Sofia. Did not have time for the Thyssen, and I know there are lots of other smaller museums. We also visited the Royal Palace, Temple of Debod, Retiro Park, San Miquel Market, and had some time to wander through plazas, squares & neighborhoods. Some people don't care for Madrid, but I loved it, and wished we had 5 nights instead of 4. Especially if you like art, would you be willing to take a night away from Grazelema? Just a thought.

We stayed in the following hotels. I think prices ranged from $130 to just under $200.
Madrid - Mercure Madrid Centro
Toledo - Abad Toledo
Cordoba - Las Casas de la Juderia
Granada - El Ladron D'Agua
Seville - Apartamentos Suites Santa Cruz

Some favorite restaurants:
La Azotea in Seville.
Mercado Barranca in Seville
El Trillo in Granada
Regadera in Cordoba (reservations are necessary)
Mercado Victoria in Cordoba
El Trebol in Toledo
Cerveceria Cruz Blanca in Madrid
Mercado San Miguel in Madrid
Cerveceria Cervantes in Madrid

This day looks tight: 3/22 drive rental car to Jerez, Cadiz, spend night in Arcos

I believe for Cordoba-Toledo, you will have to transit through Madrid. Not a huge deal, but you might want to rework it.

You might end up skipping Cadiz but that's a decision you can make on the day, as long as it's not a must-see priority for you.

Yes, you do have to change trains at Atocha in Madrid when you travel from Cordoba to Toledo. Not a big deal. We did this on our way from Toledo to Cordoba. It's very easy.