The correct option is C haven't gone
The word 'yet' means 'till now'. This means that the action has not yet happened.
Option C: 'Haven't gone' indicates the present perfect tense in the negative: it states an action that has not yet happened. Hence this is the most suitable verb form for the given sentence; C is correct.
Option A: 'Didn't go' means that an action didn't happen at all. But, 'yet' means that it hasn't happened till now, it will happen sooner or later. Hence, this option isn't suitable and A is incorrect.
Option B: 'Have gone' indicates present perfect tense in the affirmative, it states an action that has happened. But as the adverb 'yet' is present, the meaning formed is ambiguous: they have gone to the park still (yet). Hence B is incorrect.
Option D: 'Don't go' indicates the simple present tense, it states an action that happens on a daily basis. But the given sentence states an action that is yet to happen. Hence option D is incorrect.