You have been let down by more than the system. You need to be brutally honest about your dad with your social worker. Forget your T, you need a new T, she is not doing you any favors, telling you to accept the verbal abuse you are getting. You need a different T but as a minor I have no way of telling you how to do that but through your social worker and tell her about the depression and the adult family matters that you are being brought into.
A group you might find help with, even if you do not have a parent with alcholism, is the adult children of alcholics group, because they also deal with disfunctional families. I know your not an adult. I went to an adult child of alcholic meetings here about an hour away for a long time, and it was helpful.
I wish you luck. For the group therapy or single therapy, the best policy is honesty. But you have to be able to trust your therapist. I came from a disfunctional family too. I ran away from home when I was your age, just to force them into councling. I went to a shelter for runaways and had a friend of the family bring me. Don't do that, because it didn't work. But hang in there, there are many here who have been in your shoes. Hugs.