"She wasn't sure that she turned off the stove" sounds fine to me.
sure that - Google Search
Student or Learner
One of my students asked me if the below "if" could be replaced with "that". I have never heard of "that" along with "sure", but thinking about it, it could make a meaning, but I'm not sure.
Can someone tell me why that doesn't make sense in this sentense clearly?
ex)My mother wasn't sure if(that) she turned off the gas stove.
I agree with SoothingDave.
Furthermore, rather than if or that you could also use whether.
"My mother wasn't sure whether she turned off the gas stove."
It is also possible to avoid all of if, whether and that.
"My mother wasn't sure she had turned off the gas stove."
It's hard to say which of these four is the most frequently used. One hears all of them.