The following four options are literal translations of the given sentence; the differences between them concern the tone of the speech and cover some possible relations between the speaker and the listeners (how friendly/funny/sarcastic you want to be).
In brackets there is the corresponding plural version, used if the speech is addressed to more than one listener.
Zitto e in macchina! (Zitti e in macchina!)
This is direct and gives emphasis, but if said with a half-smile face, it should be funny. Note that this can be used in both informal and formal speeches, due to the absence of verbs.
Stia zitto e salga in macchina. (State zitti e salite in macchina.)
Probably the closest translation to the English sentence. It is as formal and strict as required, but also hides some fun behind it.
Faccia silenzio e salga in macchina. (Fate silenzio e salite in macchina.)
The expression "fare silenzio" is a synonym of "stare zitto", but usually it is felt to be less rude. In a standard formal speech, one tries to avoid to say "stare zitto", because it sounds inappropriate.
Le impongo di fare silenzio e di salire in macchina. (Vi impongo di fare silenzio e di salire in macchina.)
This version is usually said with sarcasm, imitating (and making fun) of some excessively formal, snooty and full of deference speeches.
If the translation needs not to be 100% literal, I would suggest also:
- Poche chiacchiere e si sbrighi (Poche chiacchiere e sbrigatevi);
- Chiuda il becco e allunghi il passo (Chiudete il becco e allungate il passo).