Hvar island takes about an hour to drive west to east and the ferry ride from Sucuraj to Drvenik is shorter (and cheaper) than the Stari Grad - Split ferry which takes 2 hours. If you are heading back to Split, it is marginal which is quicker, as it takes c 1 hour 40 to drive Split to Drvenik but if you are heading to Mostar then the Sucuraj route will be quicker.
You can't book the ferry, you just have to turn up, buy your ticket and queue. When the boat is full, they immediately start the queue for the next ferry, but there is unlikely to be a queue in May. They start loading the cars more than 30 minutes before it is due out. You can buy your ticket, put the car in the queue then walk into Split old town if you have time, but be back at the car in plenty of time.
We have found that car hire companies have not permitted us to take the hire car into Bosnia (Mostar) when renting from Split airport so you will need to check the rental terms or pay extra to get covered for Bosnia. Most hire companies also will not permit the car to be driven through the narrow coastal strip of Bosnia to get to Dubrovnik. You can go via the islands but this is time-consuming and expensive.