The correct option is D yet
An adversative compound sentence is made up of independent clauses, that function as sentences independently. These clauses contrast in meaning. In the given sentence, the two clauses contrast each other ("faced a lot of difficulties" and "smile on her face"), hence an adversative conjunction is required.
From the options, "yet" is an adversative conjunction that presents the relation of contrast between the clauses. Hence D is the correct option.
Options A and D contain an illative conjunction, used when one clause is inferred from the other. Hence A and D are incorrect.
Option B is a cumulative/copulative conjunction; "and" is used to merely add the clauses, hence B is incorrect.