I can understand that the school officials may have been over-zealous with the interpretation of its rules and expanding their definition of "campus" to include the homes of the students. However, if the home videos also showed that the homes contain illegal drugs then the school officials do have a duty to act because issues of child endangerment arise. I would contend that letting a nine-year-old have direct access to a BB gun does fall under child endangerment provisions. Having that video available so that other students can see it might also influence the other students that it was okay for each of them to attend their virtual classes with weapons that are worse than a BB gun.
I think the school officials made an appropriate response with a four-day suspension. The parents may also learn a valuable lesson from the experience. The family relinquishes a portion of their privacy rights when they allow video of the "virtual classroom" to be displayed to the school officials and other students voluntarily.