In the circumstances it is appropriate for the T to push for hospitalization if you harm the body you all reside in. Although it doesn't feel like it, you and C are actually on the same team. You just have very different positions.
But the end goal - to protect the child-self that you all once were - is the same. Punishing the self (C) was useful as some point to keep the self from being even more hurt by outside people. You insist you were never abused. C was. You helped keep her from experiencing more abuse by punishing her for ______ so she wouldn't get ______ by ______. I don't know what fills in the blanks for you, but the template for child abuse and parts is all the same, really.

You're one of the "good guys" under all that huff and puff. But you're still swinging the bat and you don't need to anymore.