Hi, leffrey weiss, there are no direct car ferries from Hvar island to Dubrovnik.
You don’t have to go back to Split.
You will take car ferry from Sucuraj to Drvenik and drive along the coast to Dubrovnik.
Car ferry can not be booked in advance. Just be in the port well before your ferry leaves and join the que.
See details of the journey here
https://www.dubrovnik-travel.net/getting-from-hvar-to-dubrovnik/