Seville is the easiest. You can bus to Jerez and visit as many Bodegas as you can before you have to return to Seville. We visited Tio Pepe (officially Gonzalez Byass) and Osbourne Bodegas. They were a short walk from each other, but there are better than a dozen Bodegas dotted around town that are open to the public for regular tours. If the RS tour includes a Sherry producer, I'd almost bet it's Tio Pepe, which is by far the biggest and most organized for large groups of visitors. We were glad we toured there but also really enjoyed the smaller Osbourne Bodega.
Jerez serves sherry (Spanish for sherry is jerez). I'm not normally a sherry drinker but it does make sense in Spain. Sherry runs the gamut from Fino, very dry and nearly clear (like a white wine), to medium sweet cream sherries like Harvey's Bristol Cream (England's QEII imports this as her favorite drink), to very sweet and dark sherries that are more like dessert wines.
I'd expect regular bus service between Seville and Jerez so you should have a pretty full schedule to choose from. The bus stations I visited in Spain all had an English speaking information kiosk that will help you sort out your options and book your tickets. Buses are cheap and nice, like what you will ride on your tour. Bus stations are more like airports, with competing companies operating out of one building.
I don't know of any wine areas close to Barcelona.
The Ribera del Duero and Rioja wine regions (known for red wines) are reachable from Madrid but I don't consider them a reasonable day trip. All the Bodegas in these areas require prior coordination to visit. If you really want to visit, a bus will still get you there and back (maybe check the TI too for an organized tour) but probably not as frequent of service and you may have to settle for a visit to a wine museum that has regular hours. The museums are old Bodegas where you can see the traditional set-up and they have wine bars where you can taste the local wines.