How does it go from vacca in Latin, and vaca in Spanish, to mucca in Italian? I'm familiar with an "m" or "b" sound becoming a "v" sound in Gaelic (specifically mh, and bh having a "v" sound in the Scottish variant), but I have never seen the opposite in effect until now. How udderly fascinating.
The two words are unrelated, as far as I can tell. "Mucca" apparently comes from Swiss-German, according to the Treccani dictionary, which traces it back to imported Swiss cows: http://www.treccani.it/vocabolario/mucca/ "Vacca" exists in Italian, but is not as commonly used now because it has picked up some negative connotations: http://www.wordreference.com/iten/vacca
It's vacca in Italian. I studied Italian for 7 years in a top NYC private school, then took Italian literature, language and culture class paid for by the Italian government for non-Italians who study Italian. I've only heard Sicilians say "mucca." Duolingo does this a lot with languages.
“Mucca” is used throughout Italy, and it actually originated in central Italy. It is very common, and many prefer it because of the potential negative connotations of “vacca,” especially in speech. Some do still use “vacca,” though, and you should find it is accepted when translating from English to Italian.