May Horse Fair in Jerez

Are tickets booked?
I was able to fly out of Sevilla and Jerez for not much more than Madrid round trip, so always check open jaw flights just in case.
If you arrive relatively early in Madrid, I would leave that day and put all your Madrid time together at the end.
I think the train route between Madrid and Toledo requires you to return to Madrid before heading to Sevilla.
It all comes down to a personal preference whether you prefer changing hotels or taking day trips, but I have to say I really enjoyed my evenings in Cordoba. But since you have an interest in Jerez, I suggest staying there and day tripping to Cordoba (or just stop over en route from Madrid).
You can't do it all, so I'd save Granada for a future trip.
I would not do a 2-2-2-2 trip, but if you have one long stay somewhere, then I am generally okay with a one or two night stay at some point.

If you find a hotel you like in Sevilla, I stay there and take the short train ride to Jerez for the horse fair each day you want to go. (You probably willmwnt to gomtwice,mat different times of the day or evening).

It for Córdoba, I would spend a night there on the way back to Madrid. This will be during Patio Festival and the streets in that area will be crowded, but worth a look. Mainly, however, Córdoba is worth some time for the Mezquita. Also, since you are interested in horses, try to get tickets for the "Passion and Duende of the Andalusian Horse" show.

https://www.turismodecordoba.org/the-passion-and-spirit-of-andalusian-horse

https://www.cordobaecuestre.com

It the most amazing and interesting horse performance we have seen, topping even Cavalia. They had a variety of demonstrations, from the type of drills, poses and moves you see done by Lipizzaners at the Spanish Riding School in Vienna, to impressive displays of equine acceleration and athleticism, to the graceful dance by two horses and the woman in the red dress ( usually shown in all the picture).

I just read the post above, and agree that it would be simplest to head straight tonToledo for your first night ( or two) then travel to Seville, then Córdoba for one night ( it is indeed very nice in the evenings), then end with 2 nights in Madrid before flying home.

You "can" fly out of Seville, but almost all flights take you to Madrid to connect to a US -bound flight, and the timing of the few flights from Seville makes it difficult to coordinate with the trans-Atlantic flight. The AVE train connects Seville with Córdoba and then Madrid, making it easy to stop for a night in Córdoba on the way.

Anne, in 2016, I ended my month in Spain in Sevilla, then 2 nights in Cordoba during the Patios Festival, then 2:or 3 nights in Jerez during the Horse Festival, then flew back to the US from Sevilla, (via Frankfurt or Munich on Lufthansa, not an everyday flight, at least then.) Enjoyed it all, and day trips would have been much less satisfying.
About the Festival del Caballo in Jerez, it is held at a special fairgrounds on the outskirts of town, a long walk from downtown, or a public bus, or taxi. It is very different during the day and after dark, when there are many overhead and intricate lighting displays. Lots of horses, riders, wagons, ladies in Andalusian gowns, great for photography. Lots of family groups, groups of friends, couples wandering. There are pavilions operated by social clubs or families, some of which welcome outsiders to sit, buy and consume food or drinks, and enjoy the music. Others are only for invited guests. All very festive! As I remember, admission was free for everyone. I am not a horse person, maybe you are. There are special events related to judging horses, award ceremonies, etc. that involve reservations, paid tickets, etc. I did not take in any of that. Hotel prices in Jerez go up during the Festival. I also enjoyed the town of Jerez, with a nice local market (mostly inside), and mildly interesting Alcazar, museum and cathedral. Some good restaurants too. The town itself was actually quite quiet during the Festival, I guess everyone was out at the Festival or sleeping it off.

As Larry makes abundantly clear, it's much better to stay in Jerez. If you day trip from Sevilla, it's an hour on the train and you need time to get to/from the station in Sevilla as well as time to get to/from the fair grounds in Jerez.

With only 10N, I would not add GrAnada, it takes too much time to get there and you need 2N. Consider going to Toledo first for 2N, then Sevilla, Jerez, Cordoba (optional) and Madrid.