What care should be taken to prepare dough and Chapatis with Rice flour?
Your mistake here was using room temperature water. Unlike wheat flour, rice flour contains no gluten to give it structure.

Instead, rice contains a starch called amylopectin (and another called amylose, but that's irrelevant here). Boiling the rice breaks the amylopectin molecules, and makes the rice sticky.

So, in order to keep your chapatis in one piece, you need to use boiling  water. Recipes I have looked at seem to suggest adding the rice flour to water boiling in a pan and stirring until it comes together.