Taking a break in the afternoon is a fine idea, for many reasons: little kids can have a nap; everyone can get a break from the heat, perhaps by jumping into a pool; and once you return refreshed to the theme parks, you can stay late and enjoy them after dark.
Epcot's huge International Showcase area is arguably at its best in the evening. Pagodas, Mayan pyramids, Parisian patisseries and other buildings representing different countries encircle a huge lagoon, and look lovely as dusk falls and the lights go on; the Tapestry parade after dark is imaginative; and the Illuminations fireworks spectacularly close the night.
Magic Kingdom also shines, after dark; you can enjoy the night-time parade, and then move near the Disney castle, to watch the fireworks and end the night. At certain times of year, the Magic Kingdom might stay open until 11 p.m. or midnight; when we visited in August, the park closed at 10 pm., which was perfect for our purposes. Note however that when daily traffic drops, the park close earlier: starting August 26th, the Magic Kingdom closed at 7 p.m., which meant no night-magic or parade.
Disney's Hollywood Studios is a hot property after darkness falls, with its flashy big-billboard style, and movie themes; and the Fantasmic show --an indescribable combo of water, lights, images, and fireworks-- is a must-see event. The Fantasmic show takes place at an outdoor theatre, which fills every night. Arrive an hour early, or purchase a Fantasmic dinner package: with this package, you first dine at a restaurant and then proceed to a guaranteed Fantasmic seat. (Be warned, however, that the special seating area is at the far right of the theatre, and seats are first come first serve.)*
As for the logistics of taking a mid-day break: they're easiest if you're staying at a Walt Disney World resort; you can simply ride a Disney bus back to your room and pool. If you're staying off-property and have a car, you can reach many hotels almost as quickly as you'd reach a Disney resort. (Remember that Walt Disney World is as large as Boston; even your on-property resort can be a ten-minute drive from the theme park you're visiting.)
If you're staying off-property and DON'T have a car, your mid-day break gets harder to manage. Most hotels offer free shuttles to the Disney parks; but there are fewer runs scheduled in the afternoon.
*Always check for updates!