Properly treated pool water appears to cause little harm to nearby plantings when splashed on the foliage. Frequent drenchings, however, do wet the soil and can lead to root rot problems. You might try mounding the soil and planting in elevated areas to encourage better drainage. Another good way to solve the water problem is to grow poolside plants in containers. Many gardeners fill in ground planters with stones or install bricks to set container plantings in these damp spots.
Lawns appear to be sensitive to pool water.
Possibly it's the large amount of water or the chemicals used. The discoloration is usually temporary but ruins the appearance of the lawn for at least a week or two. The only solution is to find another area for discharging the water. Pool water does not appear to affect trees and shrubs. You might drain the water into these plantings.