Good luck censoring the internet!
Beyond your own policies, there's not much out there to help you, or give very clear guidance. Employment law hasn't quite figured out social media, and who would win that battle if you ended up in court over it. If your employee is posting this while at work using employer resources, then you've got some acceptable use guidelines to tighten up.
Employee's family: I don't think you have any way to even pretend you can impact what they do. Aside from bringing a defamation suit against them in court, that is.
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Someone's about to get horned!