I’m finding the clockwise or counter clockwise (CCW) references rather confusing. If as stated you’re both starting and ending in Palermo, it would be a loop either way. Etna is east of Palermo (clockwise) but of course you can equally get there CCW. The difference would be doing it earlier or later in your loop. Rather than the direction of your clock, it seems to me the more important question is what size of clock do you have in mind, that is, how far west, south and east from Palermo do you envision going? You don’t have time to see everything, as you already know. What are your priorities? Taormina is beautiful, but ok to skip, however, it is close to Etna which you do want to see. Syracuse is great too, but since it’s far to the south and east that does make your clock a big one. If your clock isn’t the size of the whole island, which it probably shouldn’t be given your limited time, a clock centered to the west could include Segesta, Trapani, Erice, Agrigento, Villa Romana, back to Palermo. A more eastern clock could include at least some of Cefalu, Etna, Taormina, Catania, Ragusa, Villa Romana.