Disney HH resort: 843-341-4100
Holy Family Catholic Church, on island at Pope Ave: 843-785-2895
St. Gregory the Great: off island, very large, tons of programs for all ages: 843-815-3100
I watched a small ocean wedding performed at Sea Pines this summer. They set up chairs and a small gazebo. It was neat, but there were also all the people at the beach in bathing suits watching (and I for one was trying to stay out of the wedding photos!).
The resort could probably help you with: chairs, where to get small bouquet, a cake. You might even be able to use the room at the beach house and have it set up for just you guys, but that might also be overkill for 13 people (not sure about the charge for this either). Perhaps you could do the ceremony overlooking the marsh at the DVC resort, then back to your GV for cake and a champagne toast. Another option: dinner at one of the many restuarants at Shelter Cove afterwards. You could also use this vow renewal opportunity to take a set of professional family photos on the beach; my extended family did this last summer and it turned out great! Getting a priest might be more difficult if it's not in the actual church and if you don't belong to that particular parish. You'll have to call and ask. Again, the resort might be able to help you with some other names.
Hope it works out!