First, congratulations to you and your daughter!
It's a tough choice, nonfiction vs. fiction. I'd vote for nonfiction.
However......
As someone who has faced the realities of getting a memoir published, I'd say this: Go into it with eyes open, if it is important to you to get your book published. You'll find that agents and publishers ask tough "bottom line" questions in deciding to take on nonfiction, especially memoir.
You can face an uphill climb if your subject seems too esoteric or specialized (a concern raised with my music memoir) or if the subject has been written about before. Since there have been many memoirs dealing with addiction, you'd have to think about what makes your story different, what special credentials you may have, and so on.
(These issues are talked about in the "Life Story" forum on AW--you might want to take a look.)
If it were my story, I'd write it as memoir. I have to write what's in my heart and then worry about publication afterward. But that's not always the most practical route
You might also try writing a chapter as memoir and then as fiction told in first person, and see how it feels to you.
Best of luck, whatever you decide. The most important thing is to get writing!
Susan