It is at this point that we ran into a problem, as it became apparent that her view of the meaning of 'right' and my own were different. As best I can tell, she felt that 'right' meant that it feels right or brings comfort. I, of course, use the word 'right' to mean that an idea contains explanatory and predictive power.

These are two different meanings of the word "right". Yours is "correct fact about objective physical reality". Hers is "right for someone" meaning "appropriate [for someone]" meaning "serving well a certain purpose for that someone: e.g. making them happy".

So we had two versions of 'right'. It wasn't a given that she would accept my version, so I had to come up with a good reason why my version of 'right' was, well, 'right'.

Both are equally valid colloquial usages of the word 'right'! Your usage is not "more right" than hers. Above all avoid arguing over definitions. You're trying to get her to use a word ("right") to mean something else than she currently uses it to mean. Why? What do you care how she uses words as long as you can understand her correctly?

I suggest you describe to her that there are two different concepts, which really have nothing to do with one another, and which got confused because the two of you used "right" to mean these different things. Then you can give them two provisionally different names, and proceed to talk about the merits of each.

And remember that "what should I believe to make me feel well?" (or to achieve some other goal other than knowing the objective truth) is a valid question. The answer may sometimes be different than "always believe the objective truth". This doesn't make such a person irrational or "wrong". Believing the truth is a very common instrumental goal, but it is not a very common end-goal among humans.