One possible thing to do is to mention what those circumstances are, so the reader knows exactly what the conditions are absent which she would have acted differently, then use the word "otherwise". So in the lead-up sentence you can do something like:
"She had been under intense pressure to keep quiet about the
"Otherwise she would have raised her voice and let everyone know."
In other words, in keeping with your example:
Mention the "intervening circumstances"
[this] is what she would have done "otherwise"
"otherwise" [this] is what she would have done.
"otherwise" can mean "had the circumstances been different", however the presence of such circumstances will need to be at least mentioned beforehand because "otherwise" obviously only makes sense with contrast to another statement or fact.
I can't afford it. Otherwise I'd buy it.
^^^^^^^^^^ Imagine omitting this first part.
If you're specifically looking for one word to mean either:
without interceding circumstances.
if not for intervening circumstances.
as opposed to my suggestion, I'm sorry I don't know any way. The only way I can think of is along the lines of:
There were intervening circumstances. Otherwise she would have
Maybe there's a Latin term or something that can do this, but I really doubt it would be one word anyway.