Is inviting a friend or relative to the home considered a sin if he shakes hands with the women present in the home, or is the ruling on shaking hands restricted to him alone?

It is not permissible to invite a non-mahram (definition) man into the house if he shakes hands with women or commits forbidden acts, because that falls under aiding in sin and transgression, which Allah has forbidden in His saying: "And cooperate in righteousness and piety, but do not cooperate in sin and aggression. And fear Allah; indeed, Allah is severe in penalty."