I have three pets in my shop.

(What is the part of speech of "in mmy shop"? Is it an adverbial phrase or an adjjective phrase? Does it modify 'pets' or 'have'?)

The prepositional phrase, "in my shop," is an adverbial phrase modifying "have." The phrase tells WHERE, which marks it as an adverb.

Other questions that adverb phrases answer are WHEN? WHY? TO WHAT EXTENT?

Adjective phrases tell WHICH, WHAT KIND OF, and HOW MANY.

Another clue that it's an adverbial phrase is that it can be placed almost anywhere in the sentence.