I recommend taking a flight to Dubrovnik and flying home from Split. The reason is that going in that direction you will be able to book your island hopping ferries in advance and avoid getting up at five or six am (to queue for tickets) on the day if you travel in the opposite direction. We visited Korcula where we stayed with the redoutable Priam in Karbouni,who made us feel part of their family summer, the canoes were free and the sea clear and enticing. We also went to Mljet which was more touristy but stunning. Trogir was used to film Dr Who and is small enough to get to know in three days, Split is an extraordinary a old town built in a Roman Palace. We could do the whole thing again with a completely different list of islands.
One more thing: the ice cream parlours were to die for and there was an ice cream "barista" in Dubrovnik who juggled the scoops as he served them. We took the kids with small backpacks each and they thrived on it.
Ferries to Korcula from Dubrovnik come in to Korcula Town and some Split ferries leave from Vela Luca a bus ride down to the other end of the island. Try starting with www.croatiaferries.com/ and itinerise!
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