Yes, driving in Sevilla can be challenging, but since you are only driving out of, then back to, the train station it shouldn’t be too onerous. My suggestion is to use a navigation system to get you out of the city. Once you cross the river and are on the A-49 the rest of the drive should be pretty easy.
Bookmark El Rocío to Google maps and when leaving the train station, click on it and press start. El Rocío should be less than a 1.5 hours drive. If you don’t have free data with your phone, download a map of that area for offline use. Then, place the phone is airplane mode and it is essentially a GPS unit. No need to rent a navigation system from the rental company.
You can also use Google street view before the drive to get a feel for the route you’ll take leaving the city. It will help more than you might think since when leaving the city you may recognize landmarks you saw in street view.
Other than possibly a tour I can’t think of another option. To take a bus would take 4-5 hours each way.
Hopefully you plan on visiting a few other sites when you have the vehicle since El Rocío will probably only occupy a few hours. A couple places somewhat nearby are Dolmen de Soto de Trigueros and Castle Niebla (Guzmanes).