Drainage solution for pool area
Assuming you can pipe the water somewhere downhill, you can use a french drain if you don't want to have a exposed trench or visible drainage grates in the middle of your yard.

A french drain is a low maintenance underground trench filled with rocks and gravel around a perforated pipe, and it is usually used to pipe the water away to a lower spot or some kind of sump pump. 

They also make prefabricated french drains which is easier to install, its basically a "pipe" that you can bury and serves the same purpose without needing rocks and gravel.