P.G.
You're not a horrible mother, or you wouldn't be asking for help. You are a mother in a horrible situation. Your daughter is reflecting her home life. That won't really change until her home life changes. Therapy is great, but if the situation stays the same, it can only do so much. If there is a woman's shelter that you can contact for help, planning, etc., please contact them. Google is your friend. They may know things that you don't regarding getting out of your situation, so please don't think you have to stay until you have looked into other options.
Get some therapy for yourself because you need the strength to get out of this relationship and the self knowledge and confidence not to get back into a similar situation. Reach out for help - that means you are strong enough to ask when you need it.