yeah, the 25 yo who is jealous of the homeless 17yo, needs calibrated.
Yes and no... I went through something similar, my dad adopted a baby when I was 20. The feeling of rejection does happen. To this day, I still have a semi-awkward relationship with the fact - he's a great kid though and I've always loved children, which helped me smooth things over and build a relationship with him. That said, I managed to process things with relative ease because, among other things, I knew that his wife (he had been divorced from my mom for over a decade at the time and remarried) had always wanted a kid, but they'd had a miscarriage at one point and she was past menopause, so I could easily rationalize that the adoption was the next logical step and my dad wasn't doing that to hurt me.
With that being said, it sounds like the situation is less "adoption" and more "letting someone else's kid stay at your home", especially with said kid's dad being still in the picture and visiting often. I'm thinking there's something more complicated behind this. Her own kids probably piled on in support of their mother because the way they see it, if their mom is hurting because of it, it needs to be attacked (I've seen both myself and my sister in this kind of situation before). Mind you, I'm not saying any of them is remotely right in what they did, what I'm saying is that their behavior is coming from a different place and that they themselves will end up regretting it once they realize what it is.
Now for the bad news. Given that your fiancee is dealing with something extremely dangerous for her health, it IS going to fall on you to defuse the whole thing. (Ideally this would involve psychiatric aid, someone else to act as a mediator between the two of you.) And for that to work, you're going to need to NOT unload on her, or her kids, and be not only the bigger but far more mature of the two. Talking about it IS likely to trigger a whole lot of feelings that she isn't prepared for and that might turn to anger, but the way to work with it is to deflect and deflate her arguments slowly and calmly so she gets at the real root of the issue. You might even realize partway through the conversation what the real problem is. It DOES take a lot of patience to do this, so you'll need some time to cool off and process your own feelings towards this situation before you should even try. Assuming you can pull it off, she will talk to her kids herself about this and all of them will eventually apologize to your fiancee and the kid you guys took in. But, again, wait for some time to cool things off. If confronted, tell them that's exactly where you're at - trying to make sure you're being the fairest to everyone in this situation, themselves included.