As a result, using ‘have’ in place of had in that particular conditional clause would be totally wrong just as the choice of the tense in the main cause it is introducing should be ...

With the third conditional ... As your example illustrates, when we are discussing such past situations we normally use past perfect in the if-clause, followed by would have + past participle ...

Of course, had we used the more normal if-clause to express this conditional idea, the contracted negative form would have been the norm: If only it hadn't rained last Saturday, we would've had a ...