I think the opposite as some of these ideas.... I think in this situation you're required to judge her based only on what she does in her working relationship with you. And I think you have to do your best to treat her the way you would treat anyone else even though the alcohol issue is a personal problem. I recently worked with an active alcoholic and I was really sensitive to it and had a really hard time being around him, so I understand how it feels (luckily I wasn't this guy's boss!). But if she's doing her work and not causing trouble then I don't think it's appropriate to dive into what is still her personal life.
The drunk calls, I agree, should be stopped though since that's a concrete instance.
Either way it's a difficult position to be in and I think it's very good of you to be proceeding with empathy! Congrats on your sober time.