Gonna hafta agree with Poeman. Even if it's part of the storyline, those two islands are within miles of each other. Your storyline doesn't make it make anymore sense than it already DIDN'T. The gods sent down a beam and made one island a desert. because the trainers and rangers didn't get along? Why on EARTH would the gods care about that, especially enough to blast a whole ISLAND and turn it all barren and deserty? And since the Ice Age that apparently happened a while ago is over, that ice should STILL be melted. If it happened as long ago as you're implying, the ice should be gone. How long do you think it took to thaw out after the ice age? =_=. And if you wanna change it to the ice age being recent enough for the ice to still be there [how the hell are there humans already...], then even if the gods blasted that other island and made it a desert, it would've gotten snowed on again, seeing as that other island is still ice-tastic, meaning there's gonna be snow in that entire area.
I don't care HOW slowly the ice is melting, it would HAVE to be the same on both islands. You can't just take every illogical point in your story and fix it by saying "God/the gods did it." It doesn't work like that lmao.