The Paddock pool seems to best meet the criteria you describe. It has both zero entry and a water play area that includes two small kiddie slides. This pool also has a large water slide, life guards, and daily pool party activities. Integrated with this pool, the Paddock Grill is also a nice place to grab a quick meal, and is a convenient location for refillable mugs.
We also enjoy the Paddock section because it is a short walk across the bridge to the High Rock Spring pool and the Carriage House (front desk, restaurants, spa, gym, and boat transportation).
If you're requesting the Paddock section, you may want to include "close to the Paddock pool" in your request. The Paddock is a large section, and the furthest set of buildings is a bit of a walk.
The High Rock Spring pool (the resort's main pool) also has zero entry. This pool also has a statue of Donald Duck with some fountains and waterfalls that kids can play in. The pool itself also has both a full water slide and a kiddie slide. Like the Paddock pool, this pool is also lifeguard protected and has lots of daily activities for kids (pool party, games, etc). As well as being co-located with the Carriage House and the Artist's Palette restaurant, this pool also has a full service pool bar. (Pina CoLava, anyone?)
The Springs section is closest to the High Rock Spring pool. However, the Paddock isn't very far away. It's a short walk between the two sections across a bridge that spans the lake between the Springs and the Paddock.
You'd have similar access to both pools by asking for a Paddock room near the pool, or a Springs room near the bridge. It's very nice to be close to the Carriage House, and the Springs can't be beat in this regard. The Artist's Palette restaurant is open late into the evening for after-park meals or snacks, and the gym and spa are beautiful. The only down side to the Springs section is bus transportation. While not a show stopper, this section isn't the optimal place to catch park buses during busy periods. It's the last stop on the route, and the buses can sometimes be crowded by the time they get there. (This is especially the case early in the morning when everyone is heading out to parks.)
Even though the Grandstand pool doesn't have zero entry, don't rule it out (at least for a short visit). The interactive water play area here has a lot to see and do. This pool also has a full bar and a drink refill station.
