Searching, I found this page, which says "de armento in Sinis tabernam", which sounds to me like a (bad) literal word for word translation.
How can I express the feelings behind the English phrase, in Latin?
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I'm not aware of an existing Latin idiom with the same meaning, so I'll translate instead. The offered translation is nonsense; it has a cow, a shop, and China (the country!) but the syntax makes no sense.
Let me start with vocabulary:
These were both well known concepts to the Romans. Using elephants and Chinese imports (as some variants of the saying do) would make the Latin feel a little less natural.
With these, I'd phrase the idea as:
Sicut bos in figlina.
Like a bull in a pottery shop.