The Rehitching Ceremony is a fun event done at the Garden Grill in The Land (Epcot). You should make a PS and ask them to note on the PS that you want to do the rehitching ceremony. Then when you arrive, remind the CM who checks you in that you want to do the rehitching ceremony.
The ceremony itself is cute: your server asks each person if they will take the other as their wedded husband/wife. You say "I do." Then you kiss to the count of 100. They count to 10 by 1's, then from 10 to 100 by 10's. Normally, people around you are clapping and counting and laughing with you. Sometimes additional servers help and if available, Mickey, Pluto and Chip or Dale can be in the "wedding" party!
Afterwards you get a nice cake and a certificate to help you remember this magical moment!
When you go, I highly recommend asking if Sam (a CM) is on duty. Sam did our rehitching ceremony and I've observed him do others. He's a real ham and plays it up wonderfully! He will make sure it is a truly magical moment for you.