I have tried to plant fruit trees and crape myrtles near a couple of mesquite trees and two of my fruit trees didn't make it.So my question is: Is it better to stay away from mesquite trees?
Planting close to mesquite tree
The mesquite survives because it has an amazingly long tap root and can send feeder roots out as far as 50 feet. Since you folks have been in a horrendous drought with high temperatures, the mesquite probably became a water hog, depriving the fruit tree roots of sufficient water. This is a supposition, based solely on the nature of mesquites and the water requirements of young fruit trees.
"Taproots of mesquites are legendary, growing seemingly as deep as needed to reach the water table—often 25 to 65 feet in length. In Texas Highways magazine in 1979, Steve Wilson, then director of the Museum of the Great Plains in Lawton, Oklahoma, reported some mesquite taproots a phenomenal 175 feet long. By contrast, the taproots of most large Texas hardwoods, such as oaks and hickories, reach a maximum of three to seven feet. The longleaf pine, an exceptionally long-rooted tree, has a taproot of only 12 to 15 feet. The mesquite’s lateral roots may fan out up to 50 feet in all directions."
When did you plant them? If they were just planted this year then they wouldn't have had a chance to get established before hot weather hit and that could have been a major factor in their demise. The mesquite could have contributed by taking water, but even if you planted them somewhere away from it, it is challenging to get things established in those conditions.