The closest water parks in Seville are Isla Magica and Aquopolis. Both can be easily reached by public transport.
Parque Isla Magica
Aquopolis is primarily a water park about 30 minutes outside the Seville centre. This is a good choice if you want relaxation on a hot day for kids as well as adults. You can book online and there are lots of discounts available in the off season months. The water is clean and safe, with lifeguards on duty. You should consider carrying your own food because the snacks available inside are overpriced and there is not much to choose from. Older kids will enjoy the go kart track.
Seville also has some smaller adventure parks like Aventura Sevilla but it is quite a distance from the city. Noria de Sevilla is closer, near the Aquarium in Maria Luisa Park, by the riverside. But it is does not have good reviews