Equating an organization to "family" is the right intent.
Just as long as there is clarity and acceptance that in every family there are struggles and dysfunctions. Teach that when these behaviors show up, the family just has to work a little harder. Show a little more grace and tolerance. Never accept disruptive behavior. If a culture shift is a goal, the first step is acknowledgment.
Define what family means—as its relevance varies. Instead of utilizing the blanket term of "family," explain what this means to the organization. Many times, organizations fail to express their family stance is based on diversity while policies, procedures and rules govern the workplace which confuses many employees.