How to make a brittler, harder chocolate coating?

You'll want to temper the melted chocolate. This means holding it at 88° F (31° C) while it cools until it is completely hardened, then finally allowing it to return to room temperature (or lower) afterward.

If you temper the chocolate this way, it will be much harder and last indefinitely at room temperature.

The easiest way to temper chocolate is the "seed method", which means adding a piece of solid (never-melted) chocolate to the fully-melted chocolate after removing it from the heat source and stirring thoroughly until the temperature reaches 88° F / 31° C, and then keeping it at that temperature until you're ready to use it.

(Note that this is for dark chocolate; for temperatures for other types of chocolate and for a more detailed guide to tempering, I suggest you check out the tempering page at Cooking for Engineers.)

_{The technical explanation for this is that the temperature at which melted chocolate hardens determines its final consistency as a solid. If chocolate hardens at room temperature, it ends up forming a very weak crystalline structure that begins to melt at even the slightest rise in temperature (i.e. in your hand). Allowing it to solidify at the highest possible temperature below the actual melting point ensures that it forms a denser crystalline structure and will not melt at room temperature.}