Just my opinion, but in my writing, such thinking is NOT a battle of two ideas, but a progression of one idea into another.
So based on the person's personality (aggressive, passive, analytic, seeking compromise, etc) they have some initial reaction about what to do, and start planning that or thinking about the implications of it. Where would it lead? Would it solve the problem, or just postpone it, or make it worse?
The results of that mental exploration then inform their final decision; e.g. "I want to fight but there is no way to win, I need to compromise somehow."
OR alternatively, "No matter what I give him, in a week he will demand more. Then what, compromise again? I get a half loaf, then a quarter, then a crust of bread. Sooner or later I have to refuse, it might as well be now!"
I find complete confusion very difficult to portray in print. I believe this "progression of thought" is easier to write plausibly and provides the information to the reader that alternative courses of action were considered and rejected.
My characters are seldom confused by what they WANT to do, but can often persuade themselves to a different course of action by thinking through the details of what to do and the consequences that will ensue.