The professor's requirement that you submit for publication a paper you do not want to submit, and the advice from the Grad Studies director to submit and then immediately withdraw your paper, are both unethical, harmful, and -- for lack of a better word -- idiotic. They are asking you to:
Use false pretexts to waste the time of busy professionals who have no connection to your course or to your university; and
Risk seriously damaging your own scientific credibility by submitting for publication a work that does not live up to what you consider appropriate standards, and (if you follow the suggestion to immediately withdraw the submission) professing to do so out of a dishonest motivation.
I see this as analogous to a criminology professor making it a grade requirement for their students to call 911 and report a fictitious serious crime as a way of learning about how the criminal justice system works. This is obviously wrong, and arguably asking you to be complicit in outright fraud. In academia, your reputation and credibility as a researcher are among your most prized possessions, and I would strongly advise you to not take any action that you perceive as risking those assets, whether it's by publishing a paper you are not satisfied with, or annoying a journal editor who is a fellow member of your scientific community with spurious article submissions and withdrawals.
My recommendation is to ask for a meeting with your department chair and go carefully over the situation and the implications of what you are being asked to do, and ask them to intervene. Another option is to enlist the help of your advisor who could help you argue your case. Much would depend on whether your advisor feels comfortable intervening, on local power politics within the department, the precise level of seniority and personalities of the people involved, etc.
Another insight I can offer is a guess about the human dynamics at play here. My experience is that when the system fails to correct bad decisions of this type, the way it happens is often something along the following lines:
Your professor is a (probably senior) person with a somewhat stern personality and rigid views about education of graduate students. She is well-intentioned, but on this issue she is simply wrong.
Your department chair is extremely busy and doesn't always have the time to deal in detail with any complaint from a student, so passed the problem on to the grad studies director. However, if you insist on escalating the issue the chair may have to (perhaps reluctantly) take the time to look more into this issue and possibly intervene.
Your director of graduate studies may be a sensible person, but like many academics may be a non-confrontational person who doesn't like getting in nasty arguments with colleagues, and was reluctant to force the issue even if she disagreed with the other professor, and came up with the "submit-and-then-withdraw" proposal as a kind of cop-out solution.
I'm assuming that the people involved are mostly reasonable people who have good intentions but need a bit of help reaching the right decision. I can't guarantee that this advice will work, and it's possible that you are in a dysfunctional department where unreasonable decisions of this sort cannot be corrected very easily, but I think it's worth a try.