Yamaha RX-V3800, Integra DTR-5.8, and the Denon AVR-2808CI all feature Networking ability along with the other features you require. You may need additional amplification (one two channel amplifier) to power the second zone for the pool (this would allow both the pool area and theater to be run at once). You may be able to use the surround back channels on some of these receivers (the Integra does this, I am pretty sure) to power the second zone speakers outside.
The DTR-5.8 is probably the least expensive (MSRP) but it is only available at authorized B&M dealers. The Denon can be found for as low as $700 online.