Everybody will understand if you say:
You should not have scolded the child, shouldn't you have?
there's nothing grammatically wrong with it, but it is not usual to have two auxiliaries in this sort of tags. And I would advise you strongly not to use it in an EFL exam.
The tag is built with the auxiliary that has the most influence on the meaning of the sentence. In your example have is the auxiliary that helps build the present perfect tense, it only modifies "scold (the child)".
Should is a modal auxiliary, it helps expressing the speaker's opinion towards the action that follows (in your sentence reproach towards "you"). It influences the whole group: present perfect verb ("have scolded") plus object ("the child"). The modal takes precedence over the tense auxiliary.
You can't have eaten the whole cake, can you?
He'll be coming shortly, won't he?
Your next question might be: what about if we have two modals, in the same verb group? Well, that is grammatically impossible in English. When two different modalities have to be expressed, one of the modal verbs is replaced by a lexical verb.
Let's say we want to express the idea of advice (indicated in English by modal "should") together with ability (expressed by modal "can"). In that case we substitute the modality usually expressed by "can" by a lexical verbal that conveys the same idea:
He should have been able to finish that work on time, shouldn't he?