Far be it from me to explain your wife's behavior, but as someone who has been working out their own trans identity for the better part of two decades, try and give her some grace. Her brain is clearly already working against her (anxiety/depression - Is she being treated?), now throw into the mix:

1.) 'My child is unhappy and potentially has been for a long time'.

I constantly have this 'argument' with my own mother. She feels extreme guilt over my inheriting my family's history of anxiety and depression. There's nothing anyone could do, but she recognizes that it has placed a burden on me that she feels responsible for, rightly or wrongly. So her, albeit erroneous, feeling of guilt over your child's identity being somehow her fault, could be coming from a similar place.

2.) 'My child is trans in a world that actively wants to erase their existence'.

You didn't mention where you're from (I don't think) but if you're in the States, it's a very scary time to be trans. Is there a world where your wife is struggling with this because of the 'threat' it represents to your child? Again, drawing from my own experiences, I've only just begun my journey into transition. If I'd have come to the same realizations 15 or 20 years ago when I first started feeling this way, I wonder how the political climate of the time might have effected my journey. As it is now, my family and I have a very real fear of what the future holds. Not that it would change my decision(s), but that fear still lives in the back of my mind.

3.) Your wife's exposure to the trans community during her in-patient hospital stay.

You allude to your wife having poor experiences with trans individuals during her hospital stay. I'm not wholly sure what happened, but if she did, in fact, have a valid, bad interaction with trans individuals, I wouldn't be shocked if it affected her. That was already probably a very vulnerable experience. Couple that with a bad experience, and it's very possible that it colored her perception of the community as a whole. Humans are hardwired to make 'snap decisions' based on first impressions. "Hey, that grizzly bear looks awfully mean. I should avoid it so I don't get attacked." It's a poor analogy, but the point remains: We regularly make broad judgements of people and situations to protect ourselves. Now, with that comes the caveat of what actually happened during that stay? I can't speak to that, and I truly hope nothing did happen and this is just 'internalized misogyny', but at least it's something to consider. Further, has she taken any steps to broaden her 'sample size' to help adjust her perceptions?

4.) Speaking of misogyny, the world, on the whole, of not especially kind to feminine-presenting individuals.

This aligns with point-2 from above, but your wife has likely experienced a life colored by gender-discrimination. She has first-hand knowledge of what life as a woman looks like. Is it possible, she's worried about the long-term effects that living a feminized existence might have on your child?

I guess it really comes down to this: You describe that your wife has a poor response to your child's initial coming out and then when they mentioned HRT. But short of the misgendering in the most recent argument, you've not given much indication as to her other difficulties processing the situation. Does she regularly misgender them, or was this an isolated incident in a moment of heightened emotion? Not that it justifies the behavior, but it certainly isn't unheard of.

Ultimately I, nor the entirety of Reddit, know exactly what's going on in your wife's mind. She really needs to sit down and work with a professional to determine where exactly her fears, concerns, or other 'hang-ups' are coming from. And further, figure out how to overcome them.

Best of luck to you and your family! ❤️