I would think that they do not want pets inside due to the gift shop is tight quarters with a lot of intricate items. They may make an exception for well mannered service dogs, I would call to confirm.
Pets are fine.
This may be a problem, unless as previously stated it's a well mannered service animal, they raise and feed goats (with a little petting zoo) in an adjacent building. Definitely call ahead with that question.
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