When interviewing a family member, it’s important to think about how hard you will question a person on topics that you know they are sensitive about. How much you will press for details really depends on your relationship with the person being interviewed, the mental health of the person being interviewed, and the nature of the sensitive topic.
There’s not one answer to how far a certain topic should be pressed for an answer and the interviewer should always keep in mind how likely it was that the interviewee was personally involved and impacted by the events in question.
It’s also worth remembering that while there may be sensitive topics of which you are already aware, there may be others of which you have no previous inkling. Pay attention to body language, facial expressions, tone of voice and other clues that you may be asking about something where’s there a “story” of which you are unaware. Depending upon the reaction it may be best to make a note of the reaction and move on to something else.
This is especially true if the person has family pictures or other items which you would like to view, get images of, preserve, etc. It’s also true if the person is a close family member with whom you had a close relationship before you ever started your genealogy.