Literal translation: we should have behaved ourselves quietly.
No. It translates either to
We should behave ourselves quietly.
or
We were supposed to behave ourselves quietly.
depending on whether it’s interpreted as Konjunktiv II or Präteritum.
Your translation would be
Wir hätten uns ruhig verhalten sollen.
I do not think that behave can be reflexive in English.
If you want to keep that nuance for some reason => to conduct oneself.
Well, yes. My concern was with the translation of “sollten”. I left the rest unchanged, because it was ok for a “literal translation”. Of course, a more natural translation would not use “behave”, but maybe “keep calm” or “keep quiet”, .
Besides, behave can be reflexive (see #2):
but the meaning of the reflexive variant is not what is intended here with the german sentence.
Thanks for checking. I stand corrected.