A rule of thumb is to use the mature canopy size as a guide. A hybrid mesquite will generally mature to about 30 x 30 feet, so planting it 15 feet away from your pool decking will place the branch tips at deck edge. The Desert Museum hybrid palo verde matures to 25 x 25. Place it no closer than about 13 feet from your pool deck.

Most folks consider the mesquite a bit of a problem because of the leaflets it drops as well as seed pods. The hybrid palo verdes don't set many seeds. In April the palo verde flowers may be an issue. Mesquites usually flower a bit later.

Mesquites have very agressive roots. While they probably won't cause a pool to crack, any cracks will be found by the roots which will compound the problem.

Here is a link to information on plants that are appropriate near pools written by the University of Arizona. All are low water users. I hope this helps.

Here is a link that might be useful: Plants for Poolside Landscapes