My thoughts are, that you have put the plants under rather a transplant shock.
I don't know what your "fertilizer/native soil mix" is comprised of, or how well drained etc. Or how big a hole you dug down and sideways before planting.
But the location now - and I'm assuming you have reasonable heat in summer - is that they are getting reflected heat off the house, the path, and also from the sand.
I have no idea what sandbox sand comprises, it probably varies from area to area of supply, but it may contain chemicals, or treatments... adverse to plants.
If you wanted a hard mulch I'd think better to go with some sort of gravel or stone - doesn't dry out so quickly and is hopefully inert.

Just so I didn't mislead you, I didn't mix the fertilizer with the sand. The fertilizer(Miracle-Gro Tree & Shrub, suggested by nursery) was mixed with the native Georgia soil. The sand was only added to top 1" layer with landscape fabric underneath. I have multiple palms and trees that were planted around the same time without any problems just not in the same section(about 10ft away) as the pygmys. The pygmy palms in question do have some sort of white powder covering all the fronds. You can wipe it off with finger very easily.
FYI; the sand was brought in by truck & was said to be white sand not to contain any chemicals but can you trust what some company SAYS.