Krilo and Jadrolinija ferry companies runs ferries that connects Hvar and Dubrovnik.
You can also use ferry + bus options to reach Dubrovnik too.
There are frequent buses 24/7 running along the coast between Split and Dubrovnik, so as long as you get to mainland at any point ( say Drvenik, or Makarska or any other place) you will be in Dubrovnik within next couple of hours.
You can also take catamaran from Hvar to Korcula, stay here day or two and proceed to Dubrovnik by morning bus ( 6.45 am) or afternoon ferry if one is running on youd day of choice.
Yes Fran it is possible, the best way for day trip from Korcula to Hvar is morning + afernoon ferry >> departure 6 am return 5 pm, it is enough time to see Hvar town.
For Korcula to Dubrovnik daytrip you can also use ferry or bus or combination of both >> the earliest departure is 6:45 from Korcula and latest 4:30 pm from Dubrovnik which gives you plenty of time to explore the town.