I solved this one in the midst of writing the question, but posting so that I can find it again.
This is a book series I listened to as an audiobook about 1-2 years ago, downloaded from my library's eBooks system. At the beginning of the story, a brother and a sister (I think, maybe homeless?) are in a mall when an accident happens (I think involving a giant bear doll of some sort) and they wake up in Hell, which is something like a boarding school complete with dorms and classes. One of the kids has a ferret, and it becomes a bit of a plot point because the kids use the ferret to try to get items from the offices, and later one of the villains finding the ferret and fitting it with some sort of device (mystic contacts?) that let them see anything the ferret did so that they could use it as their own spy.
The series kind of wavered between whether Hell was serious or not. I don't think that the kids could die, but they could feel pain, and I think injuries didn't heal normally, resulting in discussions of wounds being sewn shut so that they'd stop oozing. There was some danger from the teachers, as well as the bullying of other students (with students being encouraged to tattle on their classmates by getting rewarded). The classes were encouraging something between cartoonish villainy, and legitimate evil. I have a vague memory that Lizzie Borden was the teacher of Home Economics, with her demonstrating the sewing techniques on her own skin.
For the general plotline, I think the kids were trying to escape Hell, and I think they had to travel through Dante's circles of Hell to do so, and there was some subplot going on that there was corruption and/or that one or both kids were not actually evil enough to be sent to Hell, and if that were revealed, then it could negatively impact the administration of Hell.