South Wales - Car Rental or Tour?

For the Gore Peninsula that presumably means the Gower Peninsula.

There are fairly frequent trains from Cardiff to Tenby (usually with a change at either Swansea or Carmarthen). From Tenby to St Davids there are two buses an hour from Tenby to Haverfordwest and one an hour from Haverfordwest to St David's. That latter bus continues on to Fishguard, which has a few trains a day back to Swansea and Cardiff.

Generally to plan transit in Wales use Traveline Cymru- https://www.bing.com/search?pglt=2339&q=traveline+wales&cvid=245f679c95bb4a9a931caba0c24c8da0&gs_lcrp=EgRlZGdlKgcIABAAGPkHMgcIABAAGPkHMgYIARBFGDkyBggCEAAYQDIGCAMQABhAMgYIBBAAGEAyBggFEAAYQDIGCAYQABhA0gEINTIwNGowajGoAgCwAgA&FORM=ANNTA1&PC=U531

Transit in the Brecon Beacons is quite good- from Cardiff to Brecon use the hourly T4 with a direct connection at the very new Merthyr Tydfil Bus Station. From Swansea use the hourly T6. Brecon Interchange is a very efficient hub and spoke operation.

For the Gower by public transport from Swansea see here- https://swanseabaywithoutacar.co.uk/gower/

From Brecon to Hay on Wye use the T14 every two hours- that service continues to Hereford Railway Station for trains on the main Manchester to Cardiff and West Wales railway line. The journey is under 40 minutes so an easy day trip if you want to do it that way from a base at Brecon (or even an easy day trip from Cardiff, and far from an impossible day trip from Swansea).

Dorset from Cardiff is easy- train to Bristol, then train to Dorchester or Weymouth. And there is a very comprehensive network of the 'Breezer' buses runs around the area.

3 nights to see all of St. Davids, Tenby, the Brecon Beacons, Gower peninsula, and maybe Hay-on-Wye is really pushing it, even with a car... I suggest you need to rethink this a bit. Travel times are going to be longer than you might expect.

With respect to the Rabbies Tour I personally am not hugely impressed.
You would really need to spend the previous night in Bristol for an 0815 check in at a random street stop at the Double Tree by Hilton, Redcliffe- let's say an hour in the wrong direction from Cardiff, then say a 15 minute walk from Temple Meads Station-= an 0630 start at the latest from Bristol only to pass back again 3 hours later.
Day 1- It is at least a 3 hour 15 minute drive to St Davids, surely with a bathroom break so arriving at St Davids no sooner than noon, likely later. Then the afternoon is the vague waffle of a coastal drive to suit the interests of the group. I have experience of that with 16 people- the most dominant or the biggest tippers get what they want.
You get maybe 2 hours in St David's which includes time to get and eat lunch.
I want to either know where I am going, or preferably choose on my terms. You can't suit all of 16 people.

Day 2- Morning in Tenby (not enough time to go far, let alone to Caldey Island).
Tenby to Laugharne is a 30 minute drive, and Laugharne to Carreg Cennen a one hour drive, then Carreg Cennen to Abergaveny a 90 minute drive. So the afternoon is 3 hours on the bus and also visiting two locations.

Day 3 is a bit better- 45 minutes to Hay on Wye, one hour to Ross on Wye (by lunchtime), 45 minutes to Tintern, 40 minutes back to Bristol by 1715. Say you leave Abergavenny at 0900, that is all a bit and spend a maximum two hours in Hay that is a bit whistlestop for my liking.
Say you leave Abergavenny at 0900, you have two hours in Hay maximum, and maybe 45 minutes in Ross to wander and grab some lunch. In tourism every word has an implied meaning.

Not my own personal idea of fun or even value for money. But we are all different.

Oh and you haven't got to the Gower and have just had a drive through of the Brecon Beacons (Bannau Brycheiniog).