You can try using the Google Incognito mode.. This does cut down on what others can see and may cut down on the targeted advertising pop-ups. In Chrome click on the 3 dots in the upper right, then click new incognito window.
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You may configure Chrome History to avoid this situation. Next what is your problem if your wife and you see each other information. This can be build a healthy relation.
Is your wife agree with your idea?