Is this sentence natural? Is there a situation that a native would say 君 at the beginning? (tommy_san's concerns of late have me questioning these unowned sentences...)

In what situation do you say "You be quiet."?
Do you say "You be quiet. Don't chat during class." or "You be quiet. Mary's sleeping." for example?

You be quiet to me sounds a lot more playful than just "Be quiet." I would imagine saying it to my wife or little sister after they're jokingly trying to say something bad about me in front of other people close to me.
I guess I could also imagine it being used by an angry mother hissing sharply at her son to be quiet because Mary is sleeping.
But I can't imagine it being used by a teacher. It's far too personal for that.

> Is there a situation that a native would say 君 at the beginning?

Why not? I think I saw 君 (きみ) many times as well as, say, お前. Sounds not very polite, though. :-)

It seems a lot more difficult than I expected.... I'll write what I can.

First, "君" is actually not used so often. You need to be careful when you use it, because it could sound too キザ.
"君静かにしろよ" sounds somewhat strange to me (and it's not a problem of punctuation). "お前静かにしろよ" sounds OK.

> I would imagine saying it to my wife or little sister after they're jokingly trying to say something bad about me in front of other people close to me.

In that case, I'd say "おいやめろよ" or something.

> I guess I could also imagine it being used by an angry mother hissing sharply at her son to be quiet because Mary is sleeping.

I was imagining someone saying to his friend, "お前静かにしろよ。メアリーが寝てるんだぞ". This doesn't always sound so harsh. You could use it to tell your close friend off gently.
I don't think that parents in Japan ever address their children as "君" or "お前".

Teachers would say, "ほらそこ静かに！", for example.

I think we need longer examples that illustrate the situations.

Tommy, do you suggest to avoid using 君 regardless the context? Or are there situations when it's normal/acceptable to use it?

I personally don't recommend using it. Actually we don't often use personal pronouns of the second person. If you're talking to me and you want to ask me "What do you think?", 「とみーはどう思う？」 or 「とみーさんはどう思いますか？」 would be the most natural way to say.

I never say that the use of "君" is not normal nowadays. It depends on the キャラ of the speaker. As I said above, I think it sounds a bit キザ (I don't know how to translate this word).

"君" used in poems and songs is a lot different, by the way. You hear "君" quite often in J-pop songs, but that doesn't mean that we often use "君" in everyday conversation. I once wrote in Twitter: "日本中で「きみ」って発語されてる場所を調べたら、半数以上がカラオケボックス内だったりしないかな。" It might be true!

> キザ (I don't know how to translate this word).

complacently, smugly?
There's an example in my dictionary:
ちょっときざに聞える ~ This sounds complacently.

> You hear "君" quite often in J-pop songs, but that doesn't mean that we often use "君" in everyday conversation

Ah, that's really the case! :-)
http://www.youtube.com/watch?v=ur9n7tyNkl4