Trains from Sevilla to Jerez De La Frontera and Cadiz

Too early and Renfe is the owner operator of the trains that would supply omio with their schedules. Over the last couple of years RENFE has not been following a set time when they offer tickets for sale so throw out what you read.
Going to Jerez or Cadiz is a decision that you can make when you get to Seville I would do research on those two to see if you find enough that would strike your interest. I went to Cadiz from there on New Year's Day 2019 It is ok. The Seville to Jerez or Cadiz trains are all regional or medium distance trains meaning the price is always the same they do not sell out or require an advance purchase.

Have you already planned time in Cordoba? That would be a higher priority for me than Jerez/Cadiz.

I enjoyed Cadiz; it is a very old city. However, it's not as immediately grabbing as Seville, Cordoba and Granada. I wouldn't cut those three short in order to squeeze in a visit to Cadiz.

I haven't been to Jerez because I have zero interest in sherry and no special interest in horses. If either of those is really important to you, that might be an argument for making a special effort to get there.

I'm not generally a fan of trying to visit two not-tiny places in a single day, but that's just my travel style. You may be quite different. I do think it would be a good idea to remain flexible on this day-trip until you see how much time you'll want to spend in Seville itself. Such flexibility often comes at the cost of more expensive train tickets if the day-trip materializes, but as Jazz+Travels has pointed out, in this case nearly all the train fares are fixed. There are two ALVIAs per day that would cost more, but they're easily avoided since there are so many other possibilities.

Schedules don't change much. Look at tomorrow's schedule to see how frequent they are and how long they take.

The Jerez train station is about a mile from the center (cathedral). There are several sherry bodegas more or less along the way. The Tio Pepe tour is the most fun, it's near the cathedral. If you want to see a horse show, that's about a mile from the center, more from the train station. If you go to a show, you may have trouble getting a taxi when you leave (lots of other people may want them too). The train station in Cadiz is a short walk to the center. Pick up a map and other info at the TI there. Both cities are nearly level and easy walking, not much to see in Jerez though.

Thanks for the replies, I do have several days in Seville as well as Granada and Cordoba so just looking for day trips from Seville. Sounds like I can assume that train schedules will be similar in April/May as they are now.

Sounds like I can assume that train schedules will be similar in April/May as they are now

Absolutely. There are a lot of people taking those trains.