In this sentence is the apostrophe on the right word:
'. . . celebrating Yorkshire Sculpture Park's 30th anniversary, is sure to be a testing event.' The 'Yorkshire Sculpture Park' is later referred to in the article, without hyphens.

The apostrophe is on the right word. In Yorkshire Sculpture Park, the first two words are adjectives.

With regard to hyphens, you do not need to group the words in a title when it is used as a compound adjective.

e.g. The Yorkshire Sculpture Park anniversary...