The doctors think my dear MIL will live (barring any new infections)!
When they asked to "speak to the family about her long-term condition," I must admit I did not think it would be good news.
Opening her up to get rid of the hematoma turned out to be the right call: it was the source of the infection, and it was suppressing her blood pressure. He blood pressure is slowly rising, and it looks like they will be able to do the second operation to close her chest sometime this weekend.
She'll need one more operation a week later, the ICU for another month, and various specialty hospitals for a few months after that, but if it all goes as planned, she will come home to us this summer!
If all goes as planned. After the several days where I thought she would unambiguously die this week, I've decided: I'm all right with some ambiguity!
Thank you St. Joseph!