Actually I will share my views on gender. As possibly they are germane after all.
I don't think TWAW. But neither do I think they are all a bunch of fetishistic rapists. (Some are, just as some straight men are rapists too). But most I think are people who in good faith believe they were born into the wrong gender and struggle with that.
So I am happy to call someone a trans-woman and use their preferred name and pronouns. I won't say I believe they are a woman, or that they can ever know what it's like to have been born a woman and lived that experience.
I don't want them in women only toilets, but I believe there should be gender neutral toilets readily available, for those biological males who prefer not to use urinals, for trans identifying issues or indeed for any other issue they might have. Same for changing rooms and other traditionally single sex spaces. The patriarchy and it's horrific values makes male only spaces hostile for some men, as well as for women - these men deserve protection too. Maybe even the same for prisons. I don't want a trans-woman in a female prison, in case they are indeed a fetishistic rapist, but I also don't want them in a male prison, where they might be prey to all kinds of abuse..... So a small number of gender neutral prison places should ideally be available. There wouldn't be much geographical choice (I realise it's not financially viable to create these all over the country) so if someone asked for this, even though it would probably take them 100s of miles away from their family, it would indicate they were serious about their trans identification (or whatever other reasons made them terrified of being locked in with other men).
My position used to be a lot more hard line, TERFY even. But a few years ago it changed. And the key influence was my own daughter! She is enormously empathic and right on (something I am deeply proud of). Hates all forms of prejudice, be it racial, class based, sexuality based etc. - I don't just mean she knows it's wrong, she will genuinely take action against it, even when it is difficult or scary for her to do so....
So when I saw that she thought differently from me on the trans issue, I really decided to have a rethink..... And came to the compromise position I have just outlined, which she absolutely accepts as fair enough, and not far from her own views (as a committed feminist, just like me, she doesn't actually think TWAW, nor does she want dick-slinging twats calling themselves Kylie Big-Tits predating on vulnerable women in prisons, OF COURSE she doesn't. I strongly doubt your daughter does either, OP.
The reason I said all this? If you really want to resolve things with your daughter, OP, work out why she actually thinks you are wrong. And whether there is any flex in her position, or yours. Neither of you will benefit from being partisan or singing the company song at this point.
If you are both good people,who genuinely care for others, surely consensus is possible, regarding desired outcomes at least, even if you can't fully agree on the ideology behind them.
Good luck.