nitinjain, definitely doable but a long day. We planned to do this yesterday so had all the logistics but changed plans due to rain. Leave Seville on an 8:30 MD train (@ 1hr) which was the latest departure that would get us to Jerez in time to pick up tickets by the required 11:00. You can catch this from either Santa Justa or San Bernardo but SB was closer for us. We were staying in the Santa Cruz area and took the tram down to San Bernardo.
We took a taxi to the horse show - about 5€. It's walkable (a bit over a mile) but would not advise doing it without help from our friend offline Google maps. Horse show ends about 1:30. Taxi back to station for the 2:05 or 2:38 Cercanius train Jerez - Cadiz (45 min).
Last MD train Cadiz - Seville 8:40pm (7:40 before that). Since we only went to Jerez but ended up skipping Cadiz (it was raining), can't help with beaches. This is mid- March but we got our Seville-Jerez tickets when we got to the station. No problem and gave us flexibility. And they do include a seat reservation. Jerez - Cadiz would be a Cercanius, so probably wouldn't. Hated to miss Cadiz - probably will not be back but didn't think seeing it in the rain and cold would be much fun.