If she has an alcohol problem I am telling you that no matter what, if you jump on that crazy train, you're never getting off.
Alcoholics are among the most manipulative people on the planet.
I have been caring for alcoholics for close to 30 years as a nurse, in addition to having a few kicking around in the family, so let me give you some advice based on experience.
Go about your business.
If she's ignoring you, consider it a blessing.
Do your job.
Interact with her as necessary on a professional level.
If she does not respond and it means you cannot do a portion of your job, then go the email route to her with a cc. to your boss. This accomplishes a couple of things: Your boss is aware, your boss now has documentaiton of her behavior and how it is impacting the workplace and you have documentation to protct yourself.
Make no comment to your boss about this co-worker other than what needs to be said from a work-related perspective. No joking about "the silent treatment", no eye-rolling, no nothing. Just "I am attempting to accomplish this task. I have gotten this far in the process and have asked Crazy Mary (probalby not a good idea to call her Crazy Mary either

) for XY&Z and have not received them so I cannot go any further until I have that information. I just want you to be aware of the reason for the delay".
The thing with alcoholics (or any manipulative person) is that you need to make your decisions about things, then you need to consistently act and react in the same manner. For example, as a nurse, I often have alcoholics who are waiting for their sedative during their detox period. The sedative is usually ordered every 4 hours. If someone is really agitated/uncontrollable, we have an "as needed" dose as well. However, the as needed dose is not to be given lightly. So, generally what happens is that I give the patient their regular dose. In 2.5 hours they call saying they are feeling anxious. They do not appear anxious. They have a roomful of visitors, they are talking and laughing and eating McDonald's but they
say feel anxious and want their medicine early.
So it becomes a judgement call, where I am making a decision about medicating someone who already has a substance abuse/addiction problem.
My response is, "I gave you your medicine at 830am. It's now 11am and you can have your medicine again at 1230pm. I'll bring it in then".
I can pretty much guarantee you that the patient is going to call about every 10-15 minutes for the next hour and a half requesting that anxiety medicine. And I will repeat that same sentence every 10-15 minutes (in a perfectly pleasant perfectly calm voice no matter how I may feel inside) for the next hour and a half. And at 1230pm they will get their medicine.
With alcoholics, that old adage "Don't wrestle with a pig. You'll both get dirty but the pig likes it". Don't wrestle with her. Do your job. Communicate professionally to your boss when her behavior prevents you from doing your job and let her hang herself.
Alcoholics have a way of getting everyone aorund them in a spin.
Just don't jump on the crazy train!