The correct option is D to shop
The part of a sentence excluding the subject is the predicate. The verb
in the predicate is often modified by an adverb or its equivalent, known
as the adverbial qualification in that predicate.
In the given sentence, "to shop" is an infinitive; infinitives can modify verbs, hence performing as adverbs. Here it modifies the verb " have gone"; hence it is an adverbial qualification and option D is correct. "All" is a determiner that modifies the subject "the cousins" and "have gone" is the verb, where "have" is an auxiliary verb and "gone" is the main verb. Hence options A, B and C are incorrect.