If I was you, I'd just do her job as needed. As you said, every week or so she gets assigned one or two hours of actual work. Some of that work holds you up in your own tasks. Instead of waiting, just do the work that allows you to move forward.
Given your description of Team A and your role within, there is nothing you can do to right this injustice. There are people with more clout then you that have been convinced into silence. You can impress them with your ability to work around the problem that they have but are powerless to stop.
In some ways this is no different then working with a very difficult client.
Keep in mind that she may not be lazy, just incompetent. Often times if a person does not know how to do a job they can appear lazy. Imagine trying to explain javascript to your grandmother. There is no reference and it would be impossible to do so in most cases. Can a personal assistant reasonably transition to your daily duties?