AITA for telling my wife that she can't back out now?

When I (35M) was 19, I got my GF, Natalie pregnant. We both were scared, but had decided to tell our parents together. However, next day, she had disappeared without a trace, and completely ghosted me on all our mutual socials. I had no idea where she had gone or what she did, since I didn't have her address. For all I know, she had an abortion and I didn't have a child.

I married my now-wife, Emma (32F), a few years later. I've never told her about Natalie, because what's the point of telling her about a child that may not even exist? Well, four months earlier, a social worker showed up to my doorstep with a 15 year old girl. The worker said that apparently, this was my daughter. Natalie had a huge accident, and would have to stay at the hospital for a few months or maybe even more. In the meantime, the worker found my name in one of her files and tracked me down. The girl, who I'll call Jenny, was very polite and well-behaved, though understandably very withdrawn and suppressed. I got a DNA test done, and she was indeed my daughter (not like that was in doubt, she looked like a carbon copy of me). My wife immediately promised to take the best care of her possible and make her feel as comfortable as possible. In the meantime, I asked her if her mom had any other relatives she could go with, and she said no; that it was only her and her mom. The problem is, Natalie worked at a very high-earning job, and definitely earned a lot, and thus could afford Jenny a certain lifestyle, that we, as people who are not that financially well off, can't. She obviously struggles a lot here compared to her mom's home, and is always cold and distant to my wife. It all came to a head yesterday. I don't know the exact conflict, but Jenny lashed out at Emma violently and screamed and shouted that she wasn't her mom and had no right to parent her. My wife was pissed and told me that she won't be disrespected like this under her own home and that I should immediately send Jenny away. I told her that as Jenny's dad, I'm her only living relative in the world now and that I can't abandon her.

AITA?