That's fair enough although shouldn't that be applies to all prisoners with mental health issues? I understand that you feel differently about this because of your sister's experiences but I don't see how this woman deserves special treatment over other prisoners.
I would advocate that treatment is always the better option.
If you lock a sick person in a jail for 5 years, what do you have when they get out? A sick person that's learned all sorts of new ways to hurt people. Lock them up in a hospital though, you have at least a chance of releasing a well person at the end of it.