A few thoughts:)
We have rented with Blue many times and they were all great until our last trip this past September. It was horrendous and I will not use them again until they get their act together. You may look at Lotus, which is also a local company and highly regarded.
Hvammsvik is my favorite commercial hot spring from all of our trips. You do want water shoes or sandals as the paths to get from pool to pool are rough on the feet. You can rent them there.
As for parking in Reykjavik, do you have an Airbnb already reserved? If not, I would suggest one of the hotels that has free parking. A few that we have stayed at that have this include Hotel Fron, Center Hotel Laugavegur and Center Hotel Midgardur. Otherwise you will need to use one of the parking apps and really pay attention to the time limits etc or there are parking garages.
I would not stay in Reykjavik that 2nd night a it is backtracking. Stay somewhere around Reykholt.
You say the south coast and Westmann, so I assume you mean just a few of the waterfalls and then take the ferry over? A night at Heimaey is great. I would depart in the morning though vs midday. That will give you more time to go up the south coast.
After this, I would head up to Vik and stay the night in that general area. Reynisfjara is the famous black sand beach, but there are others. At Reynisfjara there are many sneaker waves so you have to be super careful there and never turn your back on the ocean. There is a sign as you walk down and it has green, yellow and red lights to let you know the current danger level. Do NOT go into the cave under the basalt columns. Waves come in and can take you out to sea if you do that. Many lives have been lost from not being cautious here, but as long as you pay attention it is a safe and beautiful area to visit. The black sand beach extends to Vik and there are access points there that you can walk to.
You should have been able to see all of the Golden Circle on that 2nd day, so I would not stop there again. Instead I would head to the Reykjanes Peninsula and see the sights there and then head to your hotel for the night. The closest hotel is the Aurora Hotel, which is just across a parking lot from the terminal, so less than a 5 minute walk. The rates skyrocket in the summer though and they fill up far in advance. Another possible option, depending on what the volcanic eruption status is, is the Northern Light Inn in Grindavik. It is basically right next to the Blue Lagoon, about a 2 minute drive on the same road. It is about 20 minutes from KEF, so is still good for an early morning flight.