Interviewing is a technique family historians use to collect oral history. I've seen the "I Mustache You a Question" all over the internet on t-shirts, greeting cards, notepads, etc. What a fun idea for children to use to interview family members to learn about events and stories from the family's past. For the display, I found these mustache shapes and sticks in the party favor aisle at Hobby Lobby and used them as a favor for those who came to the display. It would be easy enough to make one that is a little more sturdy to use in an activity with children at home. Just take turns holding the mustache and ask another family member an interview question. If the children are very young you'll need to prompt them to ask a question. I've included some ideas, but there are more questions in published lists on the internet.
"What is your very first memory?"
"What do you like about Christmas?"
"Tell me something about your best friend?"
"What did you like about school?"
"Who is your hero?"
"What is your favorite song?"
You get the idea. Here are some links:
50 Questions for Family History Interviews
150 Questions to Ask Family Members
Interview Questions for Family History
Good Questions for Family Interviews