Hi! If you’re in Hvolsvöllur, you definitely need to see the Lava Centre Museum– it should only be a couple minutes from where you’re staying!
I think you’re good for the South Coast then. I would probably use Hvolsvöllur as a base to see some of the south coast– it’s an hour or less to get to Seljalandsfoss, Skógafoss, Reynisfjara and Dyrhólaey. Then you scoot over east to see the rest, and stay in Hnappavellir. You’d backtrack a little from Dyrhólaey back to Hvolsvöllur; you could also try to squeeze those in as you drove east to Hnappavellir.
You could decide to spend a night after that on the Westman Islands? Or see it as a day trip from Hvolsvöllur. But it might be a nice stopping point driving back from Hnappavellir; it would be about 3 hours to the ferry port from Hnappavellir. Then you could head up to the Golden Circle from the Westman Islands, then to Reykjavik, and then to the Blue Lagoon / Reykjanes at the end. That way you’re more or less heading west to east on your way back from the south coast.
Good luck and have fun!