From a long interview with Barry Sonnenfeld:
Was the ending a re-shoot? The whole movie Christopher Lloyd’s Fester is an imposter, but then in the last scene it’s explained it was actually Fester all along…
No, there was no re-shoot. Though the original ending had Fester still being an imposter. And Gomez saying, “You know what? You out-Festered Fester. And family is a state of mind and not biology. You’re the new Fester.” And at the table read, the cast rebelled. They hated that ending. And they went off into a corner and made Christina Ricci the spokesperson for them. She was probably nine at the time. And Christina came back and said to Paul Rudnick, the writer, and myself and the producer and said, ”This can’t work. The audience will be emotionally disappointed. They’ll wonder why Gomez worried about Fester for all these decades and then just doesn’t think about him anymore because he likes this guy. It’s an intellectual ending, not an emotional ending.” And she convinced us. We realized, “Oh, jeez. Maybe she’s right.” Paul Rudnick did a re-write. But that was not a re-shoot and when we first started to shoot, that was already in there. It might be slightly abrupt.
(Get Shorty, Men in Black, and the two Addams Family movies was a pretty incredible run)