This is available at the Garden Grill in the Land @ Epcot. When you make your PS for a meal (lunch or dinner) or the Ice Cream Social, tell the CM to note "rehitching ceremony" on the PS. The CM will probably not know what you are talking about and that's ok. Consider it a magical moment to educate them!
When you check-in, tell the CM at the desk you want to do the rehitching ceremony. This can be noted on your table card and notifies your server who acts as the justice of the peace.
The ceremony is simple: the server announces to everyone within earshot that your wedding was held, but he/she was not invited. So to make it OK, you are being rehitched at Disney.
You'll stand and repeat your "I do's" to each other. Then you kiss while everyone counts to 100.
They count to 10 by 1's, then it goes 10, 20, 30 and so on to 100. The CM may try to drag the count out just for fun.
You may receive a certificate of the event. At meals, people reported receiving a nice cake for dessert (not available at the Ice Cream Social).
Your experience probably will vary depending on the CM. Some do a wonderful job; others reportedly & unfortunately sort of flubbed it up a bit. Hopefully, it will be a magical experience for you.