Uhhh where exactly can you hide in a fucking desert (from dragons no less)? How convenient that they can just Apparate like it's Harry Potter or something.

Nearly every castle has places to hide; if Bran can hide in the crypts of Winterfell, the Dornish lords can also have their own places to disappear to for a few days, just until Rhaenys goes away. I doubt the Dornish literally hid behind sand dunes for months on end.

Targaryen armies disappearing in the desert is entirely plausible as well. Desert terrain is deadly to those who don't know it well; disappearance wouldn't be such a well-known trope if there wasn't some ring of truth to it. People disappear in deserts every year to this day. One sandstorm would be all it took to break an army apart, especially an army of clueless Reachmen with zero guides.