To answer your questions, the writers are terrible.
Rhaenyra has to be on dragonstone because its important, thats where she lives in the book and is her base of operations(and important things happen here). Traditionally the heir is the prince of dragonstone so that adds some legitimacy.
In an effort to villify everyone else especially queen alicent and to showcase Rhaenyra as the rightful and legitimate heir, they've added a bunch of tension and drama that does not exist between the characters they are portraying.
But the writers have hacked so many characters and changed so much shit for this show, that it does not make sense for her to be on dragonstone at this stage, she is basically retreating.