Hi,
I have not been in this situation myself, but I know people who have been going to the USA to get married. When asked the purpose of their visit, they said they planned to get married while they were there. That was not a problem. Since your fiancee is a US citizen, you are a theoretical risk to overstay, so it would be wise to have your return flight on hand, as well as evidence that you are settled in the UK. They may not ask to see any of this but it is better to have it and not need it...
There is no problem renting a car or driving in the USA on a UK licence (I do this). I do not know the rules applying to holding a license from South Carolina when she is no longer resident there (or how to surrender it). It is obviously better not to get pulled over :-) but if anyone asks for your license, I would say show the one you used to rent the car. It creates less confusion but also, the whole point is that you are both UK residents, only visiting the US. Since I presume her UK licence shows her UK address, why complicate things?
Have a nice trip.