I read this in elementary school in the late 70s or early 80s. It’s a story about a family who travels around the western US, I think in a covered wagon, putting on a variety-type show in the small towns they pass through. It is mostly about the older daughter who wanted to be treated more as an adult and fought with her mom about whether she could wear a hairstyle that did or did not show her ears. At the end of the book she defied her mother and performed some kind of ballerina act with the adult hairstyle. The parents also let each kid pick one day a year where they could break all the rules and not be punished. There was also a part about them searching for a “man with a Bowie knife” who had committed a crime. It had some funny elements and a nice family dynamic.
This is almost certainly Mr Mysterious & Company by Sid Fleischman.
That description sounds like a book by Sid Fleischman, but the title eludes me at the moment. Sing for Your Supper by Lenora Mattingly Weber is also about a family that travels around giving shows, but I don’t think it has the plot described here.
Mr. Mysterious & Company by Sid Fleischman
Mr. Mysterious and Company, by Sid Fleischman.