Hi NN. First of all it makes my heart sing that your SD has you in her life, thank god! I can't imagine where she would be without you. If I may let me give you my perspective as a young girl who grew up with an alcoholic mother, my mother got sober when I was 13, but it did a lot of damage.
Feel free to show this to the powers that be who are trying to coerce you to have your SD see her mother so soon. The damage that is already done is hard to even quantify. I don't think adults who have not grown up with this can understand how scary it is to never know what is behind closed doors. I am 48 and still deal with PTSD. I don't trust people, I assume the worst, because those life lessons are what saved me when I was growing up. I was the oldest and only girl. I grew up checking, checking, checking, smelling my mother's drinks, tending to her black eyes, sitting next to her on the porch while the other kids played. There is NO WAY that forcing this young girl to see her mother so soon after rehab is good for her is good for her, no way. Her mother is selfish and everyone seems to be worried about her and not her poor daughter. Enough. Thank goodness you and it sounds like your husband and your SD have a head on your shoulders. This poor girl needs to be taken care of and every interaction with her mother needs to be approached from a perspective as to whether or not it will be beneficial to the child, NOT the mother.