It's not necessarily that the two brains are massively different, but how that brain identifies itself. Think about sexuality, perhaps. A straight man and a gay man might have perfectly identical brains other than this, but something is obviously different to allow one brain attraction to women and the other men. No one really knows whether this is a genetic tweak, an anatomical difference, chemical difference, or something we can't detect. Having said that, I think people do see how the male brain works or thinks differently to the female brain a lot of the time although a lot of this might be stereotyping or generalising and of course there are always exceptions.

When she says that it is the brain that decides, perhaps she's not talking about a physical anatomical difference, she's talking about the brain's ability to identify with female, male or other as opposed to the body's physical state. Gender is between the ears, sex is between the legs. Imagine perhaps that you wake up tomorrow in the body of a man. Do you now feel like a man because your body is male? Probably not. So your brain has its own idea of what your gender is which, for whatever reason, does not match what is on the outside. It isn't necessarily stereotypes- as you say, a woman can do typically male jobs and be a "tomboy" but still identify solidly as female, or a man can be flamboyantly feminine and like typically female things while identifying solidly as male. It's just that sometimes people know something isn't right and feel inside their souls that they were meant to be something else. A gut feeling. Again, no one knows why this happens, although there may be many theories. It may not make "sense" or be "normal", but then again so many things in humankind and the world don't- non-heterosexuality, genetic disorders, etc. It just happens.
As an aside, as far as memory serves, X and Y chromosomes are not the only part of our DNA that determines our physical sex, there are in fact a few different pieces that all come together and are usually in agreement but occasionally I believe you can get XX males and XY females if the other parts are in agreement on the opposite but this is rare. Perhaps something like this can result in the development of a different brain to physical sex.

Basically, your daughter is placing a higher value on this brain gender than on physical sex. I don't know how well she explained it but I hope I haven't confused you too much although I might well have done. I understand your wariness about using the wrong pronouns. I admit I find it painful when people use the pronouns of my biosex but I guess I don't expect people to be psychic.

I'll stop now I think, lol