Driving from cadiz to jerez vs train or taxi

The public-transportation route would start with a train to Jerez (only 33 minutes, but the first train you could take leaves at 10:40 AM on weekdays; of course, it's possible you couldn't get to the trains station much earlier than that, anyway). A round-trip to Jerez would cost 10 euros per person using most of the trains (a few are substantially more expensive) if you bought the two tickets at the same time. If you wanted to remain flexible on the return time, the tickets would be 6.25 euros each way.

Arcos de la Frontera would be the most convenient of the white towns most often visited. From Jerez to Arcos you'd need to take a bus; Arcos has no rail service. There are multiple bus companies serving the Jerez-Arcos route. The CMTBC schedule is here. "L-V" means Mondays to Fridays. "S-D-F" means Saturdays, Sundays and Holidays. The weekday Damas and TGComes schedules are here. You can change the date at the top of the screen to get the Saturday or Sunday schedule. I'm not sure whether CMTBC is somehow related to one of the other companies, but in any case, you can see that bus service is frequent.

Still, given that you have a mandatory return-time to meet your cruise departure, I wouldn't try to go to both Jerez and Arcos by public transportation. I don't think you'd have time to really see either one if you did that; you'd have all eyes on your watches the entire time. Arcos is not a tiny place, and it's hilly, which slows down ones sightseeing. If you decide to stick with public transit, I'd choose either Jerez or Arcos and then spend some time in the Cadiz historic area if you return early. Obviously, Jerez would be a lot easier than Arcos.

I have no experience renting a car in Europe or hiring a taxi for sightseeing like this in western Europe, so others will have to comment on those means of transportation. A taxi will not be cheap, because you'll either have to pay him to wait for you while you visit Arcos (which will take some time, and you might even want to have lunch there) or you'll pay for him to drive the round-trip twice. I'd assume a rental car would be less expensive, but you'd have to do your homework about driving rules in Spain.

There are a couple apparently free public parking lots a few blocks from the Fundación Real Escuela Andaluza Del Arte Ecuestre. If you drive, you may want to locate them ahead of time, or plug them into your GPS, or save them to Google maps. Sandman Sherry is next the the school. No idea if it offers tours. There are a number of public lots in the city, but to decide which to use, it would be helpful have already have located the places you want to visit. Jerez can be confusing to drive around since there is no organized street plan. The Alcazar in Jerez is worth visiting, but it isn’t near the equestrian school and there is limited street parking near it. For time planning purposes, Cadiz to Jerez de la Frontera, while only 14 miles, will probably take about 30 minutes to reach. From Jerez to Arcos it’s 19 miles, but it will about a 40 minute drive. From Arcos back to Cadiz it’s 31 miles, but will take a good 45-50 minutes. The times are estimates and don’t take into consideration that you may get turned around, or the time it will take you to find parking.

Thank you both so much for the information!

First make sure that there is a horse show on the date. They are only a couple times a week. Without a show, I don't know if it's worth it to visit the school, though the grounds are pretty. I toured this sherry bodega about 5 years ago when reservations weren't necessary. It was very interesting and they had a parking lot. It's about 35 minutes' drive to Arcos and well worth visiting. Note that it's perched on a very steep hill. It's very hard to drive into the historic center and there's little parking available. It's best to park in the large lot at the foot of the town and either walk or take the shuttle up to the top. Even at the top, there's a good bit of uphill/downhill walking. The RS book has a very good self-guided walking tour. Eat lunch in Jerez or Arcos - tapas is usually very small portions of "regular" food. If the hills of Arcos sound daunting, consider spending the time in level Cadiz. In that case, take the train to Jerez and taxis to/from the school and bodega tour.