A would only be correct if the sentence started "If it HAD rained we would have cancelled the picnic and GONE to the pub. The event is over. It didn't rain, but if it had, we would have cancelled the picnic and gone to the pub. The second option could be used if you're discussing habitual actions in the past: We would have picnics every Saturday when I was a child. If it rained, we would cancel the picnic and go to the pub.

I agree with Luigi - a second conditional sentence does not refer to the past. Technically, answer B fits. Answer A fits third conditional, which is about the unreal past. Don't be misled by the verb in past tense; we also use this for hypothetical situations in the present. However, it sounds very strange and confusing to use second conditional in this context, so I also agree that the question is faulty. Perhaps we don't treat weather conditions with such unlikelihood.

(Ps: I'm not a native speaker) A sentence with the 2nd conditional does not refer to the past, It is just used to talk about an impossible or an unlikely situation In the past it would have been "If it had rained, we would have cancelled the picnic etc.." ;)

There is a problem with the question, not the answer. The question (gapped sentence) is wrong. It should read: If it had rained .................. the picnic and gone to the pub. This is a third conditional about a hypothetical situation in the past, and the correct missing form is 'we would have cancelled'.