You are not permitted to take communion because you are not in communion with the Church. It's not a matter of "not performing certain required works," but simply a recognition that you hold yourself outside of the Catholic communion. For you to receive communion but remain outside of the church would be to say one thing but do another.
My children can receive it
Presumably you don't object to that. :-)
the Mafia and all the Kennedys can receive it
It's Catholic teaching that persons in the state of (unrepented) mortal sin must not receive. We can debate to what degree a person's subjective guilt may be diminished by ignorance or other circumstances, but objectively, persons who commit the kinds of crimes we would associate with the Mafia, or who cast votes in Congress in favor of abortion, should not be receiving communion.
So what you say here is not really correct.
but I, along with some of Catholics' favorite authors, such as C.S. Lewis, and the authors of the hymns Catholics sing, such as Charles Wesley, could not or cannot.
Back to what I said at that top.
But there's a very simple solution to this; it's called a "spiritual communion". When your family members go up to receive, simply pray to Jesus and ask him to give him every grace he could give you by receiving Catholic communion. He will never respond to such a request in any but the most lavishly generous fashion. Trust me.
"..but objectively, persons who commit the kinds of crimes we would associate with the Mafia, or who cast votes in Congress in favor of abortion, should not be receiving communion."
Unless they've gone to Confession first.