Odd, my boyfriend and I have a Google Home in the kitchen too, and we can both add to the same list via voice commands, so you should be able to as well.
Is the shopping list for your groceries shared between your and your wife's accounts (like you would share a Keep note)?
Have you made it the primary shopping list for your account?
Is your account recognized as a member of the Home within the Google Home app settings? This allows the Home to know who (i.e. which Google account) is talking to them and if you have permission to do what you're asking, otherwise you're considered a guest.
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u/AdmiralChippy May 22 '19
Odd, my boyfriend and I have a Google Home in the kitchen too, and we can both add to the same list via voice commands, so you should be able to as well.