FP, if your niece looked like a transwoman instead of a woman would that make your case in support of her the weaker?
The way people look, and whether 'anyone would know' is really not the issue. A lot of transwomen look fairly obviously male, whereas someone like Courtney Act looks very feminine and glamorous, but that doesn't make him a woman (as he acknowledges - sometimes he is Courtney and at others he is Shane). The ability to 'pass' doesn't make someone more of a woman than someone who will always look like a man. I don't know why you think what someone looks like makes a difference.
Your niece may indeed 'pass' as a woman, but the fact remains that there could be women she cares for who would be very unhappy to know that they were being cared for by a male. I'm sure that many others won't mind at all, but there are religions which would absolutely forbid it, and regardless of religion people's choices have to be respected. If women can't stipulate whom they allow to touch them intimately, where does it end? Are we to simply submit to male wants in all circumstances?
It is that sort of thinking (that if women don't know they are being touched by a man then it doesn't matter) that is so misogynistic. It totally foregrounds male wants and renders female needs irrelevant. Can't you see that? I am not for a moment suggesting that your niece is anything other than a marvellous carer, but that is not the point. IMO transpeople (male or female) should avoid careers where they need to touch others intimately. This leaves them plenty of choices and respects the fact that people in care have agency.