I have a 9 yo and a 6 yo.
They both knew long before I said anything to them about their dad, that there was an issue.
They didnt know about the drinking but they did know about the excuses he made to bail on plans, the sleeping elsewhere when he lived at home with us rather than admit to having been drinking, the short temper, the cold/hard attitude toward anything and anyone other than what he wanted in the moment....
So by the time I spoke to them and then later, a therapist spoke to them, about the disease and why we would not live in the same house with him anymore and what the deal about visits was (court order), they already knew....
Kids are VERY perceptive and get it. My kids are far far far less anxious with limited interaction with their father than they are when they see him more often.
I applaud you for setting a boundary about what you and your daughter will tolerate and for planning to stick with it.
The silent tension and walking on eggshells and wondering what might happen from one day to the next that is all life with an A, is intolerable to us as adults and we have the ability to come here and talk and ask questions and read and understand. Imagine being a kid and sensing all the same stuff and wondering what's going on but having no knowledge of what is happening and how scary and confusing that has to be.
You're giving your daughter a gift by setting a limit with your AH. Bravo to you!