Under the circumstances, there is no possibility of having a normal and healthy relationship - the circumstamces simply don't permit this. However, it is possible to make some progress on the interaction between you and your daughter during the contact that is allowed. The situation she is in, all by itself, is sufficient reason to pursue some therapy, and I would imagine the Court would support such an intervention (regardless of where the therapy occurs). I'm not so sure it's reasonable to ask the school to do the therapy, since there's only so much that should be asked of schools. However, if the school is willing there is no reason it can't occur in that setting.
I'm not a doctor, but I am experienced in family court.
You don't state why you have supervised visitation, and you don't state your "legal" custody status. If you have joint legal, you can SUGGEST to mom the child go to counseling, you cannot force the issue with her unless you file a court order demanding she put the child in counseling.
If you have no legal custody, you have no say whatsoever in her medical/psychological well being.
Again, with little facts, there is no way to help you.