OP, firstly - your issues around anger/ what triggers it/ your feeling of intense frustration at your childs completely normal/ child like behaviour - sound as though they run deep. So - rather than beat yourself up for that, I think you need to accept that therapy doesn't change someone in a really fundamental way in only three months.
If it's not minor issues you are dealing with, then it won't be minor changes that are needed.
Really importantly - is your counsellor good enough? I remember, when I had counselling that after a few months I got very upset and frustrated and said to the therapist - okay, so I see why I have these feelings, but that's not good enough, we can talk forever about that - but I still have them. I don't want to have them. But she just nodded - because she knew that that stage takes time...
You need to completely reframe the way you look at the world, dig very deep into your core beliefs and change those - and it is possible, but it's not easy or quick.
So - you are on a journey - and tough as it is, you need to keep going.
You are angry with your daughter - but her behaviour is standard, its actually part of a child growing up and dealing with the world. You seem to expect adult level, rational behaviour from her. You cannot control her behaviour to the extent you are trying to, except through serious threatening/ frightening of her - which is what abusive parents do.
And you are not abusive and you don't want to do that.
I think that if you feel there is no joy at all in the world then you really are depressed. I would really suggest you get onto AD's. Is your counsellor good enough?
Are there any practical steps you can put in place, any thought experiments you can conduct that can protect you and her until you are further along this journey? ie. help with her/ less time with her....