In part it depends on what you mean by "corpus analysis". However, if you only look at the texts, it is impossible to determine whether the A→B mapping was influenced by the A→C mapping, or vice verse. The first step would be to establish that B was available to the translator of C, or the opposite. Without text-external evidence regarding the creation of the texts, you can't establish chronological precedence.
An obvious problem is that a certain original text may only have a single reasonable translation from Lg(A) to Lg(B,C). Influence can only be detected text-internally by looking at similarities, not dissimilarities. In case both texts contain an undeniable similarity and both translations are clearly in error, then a relation of influence is highly probable. However, it is necessary to independently establish that the translations are in error, meaning that you have an independent way to validate the translation. Even assuming a single original text being worked from, translations (especially good ones) often do not mechanically convert language-to-language based on original words, they re-express the original ideas in the target language. One therefore has to rule out the possibility that a similarity that is not trivially derived from a common source text A could also be the result of an ideological similarity shared by the translators. This is unlikely to be an alternative explanation when the similarity is plainly wrong on linguistic grounds (there is an example in translations of the Bible into Logoori, where the 1967 version contains a typo, or less probably, a typo plus a significant grammatical error – dunno what was in the earlier versions, but if it is also in the 1950 version, I would vote for "copying" rather than "coincidence; linguistic necessity").
