That is a very difficult decision to make. Is your daughter at all willing to try to get better? Will she take meds for the hallucinations, and talk about what is going on? Cutting is generally a way that people try to cope when they don't know how else to cope. It may be taken as a sign that she wants her life to be different, and that she wants help. Hospitalization is usually more about keeping people safe than really treating mental health issues, or perhaps medication stabilization if it is the only way to accomplish that.

What other options have you considered? Have you tried intensive outpatient programs or residential treatment with an objective to help her to learn how to manage her problems and live in the real world? I don't know your daughter, or you, but I would make sure that all other options have been explored before turning to long-term hospitalization. If she is able to be safe, I would look for other answers. If she isn't safe, she may need to be in the hospital until she can be stabalized.