Personally -- I wouldn't sponsor her, because sponsoring her -- I'd have to also sponsor her mom & dad -- and I don't do families.
It would be tough enough sponsoring her -- but w/ the parents interfering -- how are you going to handle that? I'd be too tough on her and on her parents -- so, I wouldn't get involved in it.
I'm guessing your alcoholic, and she's alcoholic and pill-head, too. It also sounds like she may have doctor problems or health problems -- and she knows which docs to see to get the pills she wants. So, then, you're in the middle of the doc, the parents, and her.
It get's real sticky because it could also get legal -- because you can't give her medical advice or suggestions -- that's against the law. Plus, we don't "give medical advice".
I know what my sponsor would say, -- if she were to ask him to sponsor her -- (he's in his 80's, over 50 yrs sober, and yes, he sponsors women, too) regardless if she was man or woman -- he would tell her "I don't sponsor anyone on pills. I don't have any experience w/ that, and I'm not about to give you medical advice. You'll need to find someone else to sponsor you, that has experience w/ the pills."
What would I do or say? I'd say the same thing that my sponsor would say...
I have had some experience sponsoring some -- who were on meds. However, I didn't have to worry about family interference, and in the end, it worked out okay while it lasted. (The sponsor relationship).
I don't know if that helps you at all or not. I hope so. I certainly do not envy your position. If it were me... I would say no.
btw: have you talked w/ your sponsor about it?
Best wishes, and if I can be of help, let me know.
Also -- welcome to the forum! And, thank you for your participation!