I agree with bookwyrm. Your D only knows this life and for her that is normal.
I felt the same way growing up with my AF, and aslo I had some very similar conversations with my 12 yo D when I decided to leave my, now recovering, AH.
Of course your D knows something is wrong, but she thinks that's not a big deal, as she doesn't know better, and aslo it's been like that forever and you all survived so it can not be that bad. My D even told me: why are you making such a big deal out of it, he is just being dad, and BTW everyone lives like this!!!
When talking some more to her I discovered she is not even angry with him, after all he was just being himself, but with me because I was the one that keeps agruing and making a big deal of it all.
All of that was pretty much a slap in my face, and I realized it is my job to teach my kids what "normal" is, or better to say to show them different, healthy kind of normal. So I did. In the meantime AH became RAH, and moved in back with us, and my kids are larning a new normal in thier life. All of this is happening only recently, but I can already see a great change in them, as they're learining for the first time in their life what a proper role of someone's father is.
If he didn't start recovery than our kids still couldn't learn about what the real dad is all about, but by me removing them from that kind of life, they could still learn what is unacceptable.
IMO the biggest problem for kids growing up in alcoholic enviroment is the fact they never learn what normal really is, they only learn twisted dysfunctional patterns.
IMO you can expect your 15 yo to know that removing an active A from her life is a good thing, it is your job to teach her that by example.
Once I got strong and healthy my kids started to bounce back, once their dad started to work on his recovery, it made the things even easier for them, but again even if he didn't do that I'd have to do it myself, it would be harder but not impossible.
The first thing I needed to do is teach my kids to trust me, as to be honest before they had no reason to, as all I was teaching them (by example, and BTW that's the way kids learn) is misery.
Also, I strongly suggest you read on ACOA forum and not take any of it lightly. It doesn't take an abusive A, functioning one is enough too (as mine AF was) to leave kids scared for life.
And, you D doens't have to agree with you right now (she most probably will not no matter how hard you try to explain it), but if you stay strong and positive, she'll learn soon enough. It's simple: you're the parent, you know better ( it took me an awful long time to realize this).
I believe you're going in the right direction,
I wish you well
HUGS
PS Of course all of this is just my opinion, so you take what you like and leave the rest.