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In general, there is some flexibility as long as there is no reason to suspect you lied specifically to circumvent the regular procedures and never intended to travel to Italy. It's even less of an issue for a multiple-entry visa (which is by nature not tied to a specific trip). See also Can I use my Schengen visa for a completely different purpose and entry point?
For your wife as the member of the family of an EU citizen, it's even less of a problem. As long as she is traveling with you, the visa is merely a formality, where she is traveling is not relevant to the decision to grant entry or not. She can only be denied entry if she is not who she says she is (e.g. she is not your wife or you're not an EU citizen) or if she is a threat to public policy, public security or public health. In principle, you should not have had to justify the purpose of your trip or much of anything else when applying for that visa.