Victorian setting fantasy about an adopted girl with magic powers rescuing her birth mother.
I remember reading this book when I was younger, and it still really sticks with me. I would have been 8 to 12, and I'm a girl living in England. Probably read it in the early 2010s. It was probably a library book. I read a lot of books back then, so it's possible my brain is meshing a few together, but I think these were the key points.
A girl is adopted by a rich family. She and her adoptive siblings have magic powers, but she's the best at it. I think her name was either Ella or Rose, but I'm not sure. She finds out that her birth mother is still alive and being kept hostage in this warehouse type place, and that her birth name was Hope before her mother managed to get her out of the warehouse to save her as a baby. She and her siblings sneak into the warehouse by making themselves invisible, but the mother senses them, and uses her own powers to reveal the little sister, who's the weakest at the magic. The mother, at first, wonders if the little sister might be "Hope?" but realises it can't be because "she'd be older" or something like that, but she starts interrogating the sister, like "how did you get in here? who are you? who sent you?" so Ella/Rose reveals herself, and manages to free her mother. I seem to remember the girl using a piece of broken mirror to cut through the magic bonds that were stopping her mother from escaping. And I also remember, at some point, one of the other siblings getting annoyed that the mother kept calling the girl "hope" instead of her new name.
I have this vision of the cover featuring a victorian era old timey street lamp, and being purple/pink, but I honestly don't know where that vision has come from.