First of all note that this is a labor issue. You are an employee of the university, given a certain work assignment which you are unable to properly fulfill, but expected to do so anyway. Even though the university cloaks it it the garb of "student" affairs.
Secondly, note that the university is linking your being a PhD candidate - a junior researcher - with teaching, to the extent that the junior researchers are, as they see it, obliged to teach whatever the university/department deems it necessary for them to teach. This is not problematic in itself - assuming you're not required to teach things you are not academically mal-equipped to teach; and provided your entire activity as a PhD candidate - research + teaching + administrative duties etc. - is considered altogether as your breadth of employment. In a typical US university, that is not, unfortunately, the case.
So now that we've established the scenario, the question becomes: What is a semi-uncrecognized, disenfranchised, employee for a large (academic) institution to do when demanded to perform tasks s/he cannot properly perform?
Unfortunately, many junior researchers bow their head down, swallow their pride and try to teach / TA the course as best they can. The result is a reinforcement of their collective servility, a deterioration in teaching quality, and indirectly also a push-down of employment conditions, since the university, when faced with lacking of qualified teaching staff, is under no pressure to offer better employment conditions so as to be able to recruit (especially on short notice).
Now, what I would like to be able to tell you is: Go see your academic staff union representative. The union should be raising hell on this kind of demand, calling out that DGS and threatening both collective action and initiating academic-disciplinary procedures against that DGS.
However, most US universities are not unionized, and even if yours was - the fact that this can happen means that the union is weak or co-opted (or both). So, what you should really focus on doing is unionize junior academic staff at your university. I know that is a tall order, and certainly it is not a matter for a single individual, but it is an absolutely necessity, and such struggles do succeed when carried out consistently.
Lacking a union - you need to find an officer or an organization which would be interested in putting counter-pressure on that DGS. Options could be:
- The instructor in charge of the course.
- The university's student union, or more specifically its departmental officers/representatives.
- Your advisor.
- Some Dean or vice-Dean in charge of teaching, as opposed to graduate studies.
- A senior tenured professor whom you have a close relationship with.
- Your cohort of junior researchers at the department.
These were not listed in order. The question of who to approach depends on your relationship with them, your assessment of their interest and willingness to act on this matter, their backbone, their ability to withstand pressure etc.
About the last option - it is the most relevant if there are multiple junior researchers who have been met with this demand. Try to locate a group of people in the same predicament. You would be amazed at the difference in effect of even 3-4 people coming to see the DGS together, to explain how they cannot ethically teach courses in material they are themselves not fluent in, relative to a single person coming to complain or ask for leniency. It would be even more powerful if that group could get a few more PhD candidates to tag along, fill up the DGS' room, and look seriously dissatisfied.